maple.mw

> restart;
int(arcsin(x)*log(x),x);
 

`+`(`/`(`*`(`+`(`-`(`*`(2, `*`(arcsin(x), `*`(tan(`+`(`*`(`/`(1, 2), `*`(arcsin(x))))))))), `-`(`*`(2, `*`(`^`(tan(`+`(`*`(`/`(1, 2), `*`(arcsin(x))))), 2), `*`(ln(`+`(`/`(`*`(2, `*`(tan(`+`(`*`(`/`(1...
`+`(`/`(`*`(`+`(`-`(`*`(2, `*`(arcsin(x), `*`(tan(`+`(`*`(`/`(1, 2), `*`(arcsin(x))))))))), `-`(`*`(2, `*`(`^`(tan(`+`(`*`(`/`(1, 2), `*`(arcsin(x))))), 2), `*`(ln(`+`(`/`(`*`(2, `*`(tan(`+`(`*`(`/`(1...
(1)
 

> restart;
int(x*arcsin(x)/sqrt(1-x^2),x);
 

`+`(x, `-`(`*`(arcsin(x), `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))))) (2)
 

> restart;
int(arcsin(sqrt(x+1)-sqrt(x)),x);
 

`+`(`-`(`/`(`*`(`+`(`*`(`/`(1, 16), `*`(arcsin(`+`(`-`(`*`(`^`(`+`(x, 1), `/`(1, 2)))), `*`(`^`(x, `/`(1, 2))))))), `*`(`/`(3, 8), `*`(`^`(tan(`+`(`*`(`/`(1, 2), `*`(arcsin(`+`(`-`(`*`(`^`(`+`(x, 1), ...
`+`(`-`(`/`(`*`(`+`(`*`(`/`(1, 16), `*`(arcsin(`+`(`-`(`*`(`^`(`+`(x, 1), `/`(1, 2)))), `*`(`^`(x, `/`(1, 2))))))), `*`(`/`(3, 8), `*`(`^`(tan(`+`(`*`(`/`(1, 2), `*`(arcsin(`+`(`-`(`*`(`^`(`+`(x, 1), ...
`+`(`-`(`/`(`*`(`+`(`*`(`/`(1, 16), `*`(arcsin(`+`(`-`(`*`(`^`(`+`(x, 1), `/`(1, 2)))), `*`(`^`(x, `/`(1, 2))))))), `*`(`/`(3, 8), `*`(`^`(tan(`+`(`*`(`/`(1, 2), `*`(arcsin(`+`(`-`(`*`(`^`(`+`(x, 1), ...
`+`(`-`(`/`(`*`(`+`(`*`(`/`(1, 16), `*`(arcsin(`+`(`-`(`*`(`^`(`+`(x, 1), `/`(1, 2)))), `*`(`^`(x, `/`(1, 2))))))), `*`(`/`(3, 8), `*`(`^`(tan(`+`(`*`(`/`(1, 2), `*`(arcsin(`+`(`-`(`*`(`^`(`+`(x, 1), ...
(3)
 

> restart;
int(log(1+x*sqrt(1+x^2)),x);
 

`+`(`*`(ln(`+`(1, `*`(x, `*`(`^`(`+`(`*`(`^`(x, 2)), 1), `/`(1, 2)))))), `*`(x)), `-`(`*`(2, `*`(x))), `/`(`*`(`^`(5, `/`(1, 2)), `*`(arctanh(`+`(`/`(`*`(2, `*`(x)), `*`(`^`(`+`(`-`(2), `*`(2, `*`(`^`...
`+`(`*`(ln(`+`(1, `*`(x, `*`(`^`(`+`(`*`(`^`(x, 2)), 1), `/`(1, 2)))))), `*`(x)), `-`(`*`(2, `*`(x))), `/`(`*`(`^`(5, `/`(1, 2)), `*`(arctanh(`+`(`/`(`*`(2, `*`(x)), `*`(`^`(`+`(`-`(2), `*`(2, `*`(`^`...
`+`(`*`(ln(`+`(1, `*`(x, `*`(`^`(`+`(`*`(`^`(x, 2)), 1), `/`(1, 2)))))), `*`(x)), `-`(`*`(2, `*`(x))), `/`(`*`(`^`(5, `/`(1, 2)), `*`(arctanh(`+`(`/`(`*`(2, `*`(x)), `*`(`^`(`+`(`-`(2), `*`(2, `*`(`^`...
`+`(`*`(ln(`+`(1, `*`(x, `*`(`^`(`+`(`*`(`^`(x, 2)), 1), `/`(1, 2)))))), `*`(x)), `-`(`*`(2, `*`(x))), `/`(`*`(`^`(5, `/`(1, 2)), `*`(arctanh(`+`(`/`(`*`(2, `*`(x)), `*`(`^`(`+`(`-`(2), `*`(2, `*`(`^`...
(4)
 

> restart;
int(cos(x)^2/sqrt(cos(x)^4+cos(x)^2+1),x);
 

`+`(`-`(`/`(`*`(2, `*`(`^`(`+`(`-`(`*`(`+`(`*`(`^`(cos(`+`(`*`(2, `*`(x)))), 2)), `*`(4, `*`(cos(`+`(`*`(2, `*`(x)))))), 7), `*`(`+`(`*`(`^`(cos(`+`(`*`(2, `*`(x)))), 2)), `-`(1)))))), `/`(1, 2)), `*`...
`+`(`-`(`/`(`*`(2, `*`(`^`(`+`(`-`(`*`(`+`(`*`(`^`(cos(`+`(`*`(2, `*`(x)))), 2)), `*`(4, `*`(cos(`+`(`*`(2, `*`(x)))))), 7), `*`(`+`(`*`(`^`(cos(`+`(`*`(2, `*`(x)))), 2)), `-`(1)))))), `/`(1, 2)), `*`...
`+`(`-`(`/`(`*`(2, `*`(`^`(`+`(`-`(`*`(`+`(`*`(`^`(cos(`+`(`*`(2, `*`(x)))), 2)), `*`(4, `*`(cos(`+`(`*`(2, `*`(x)))))), 7), `*`(`+`(`*`(`^`(cos(`+`(`*`(2, `*`(x)))), 2)), `-`(1)))))), `/`(1, 2)), `*`...
`+`(`-`(`/`(`*`(2, `*`(`^`(`+`(`-`(`*`(`+`(`*`(`^`(cos(`+`(`*`(2, `*`(x)))), 2)), `*`(4, `*`(cos(`+`(`*`(2, `*`(x)))))), 7), `*`(`+`(`*`(`^`(cos(`+`(`*`(2, `*`(x)))), 2)), `-`(1)))))), `/`(1, 2)), `*`...
(5)
 

> restart;
int(tan(x)*sqrt(1+tan(x)^4),x);
 

`+`(`*`(`/`(1, 2), `*`(`^`(`+`(`*`(`^`(`+`(1, `*`(`^`(tan(x), 2))), 2)), `-`(`*`(2, `*`(`^`(tan(x), 2))))), `/`(1, 2)))), `-`(`*`(`/`(1, 2), `*`(arcsinh(`*`(`^`(tan(x), 2)))))), `-`(`*`(`/`(1, 2), `*`... (6)
 

> restart;
int(tan(x)/sqrt(sec(x)^3+1),x);
 

`+`(`-`(`*`(`/`(2, 3), `*`(arctanh(`*`(`^`(`+`(`*`(`^`(sec(x), 3)), 1), `/`(1, 2)))))))) (7)
 

> restart;
int(sqrt(tan(x)^2+2*tan(x)+2),x);
 

`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
`+`(arcsinh(`+`(tan(x), 1)), `/`(`*`(`/`(1, 10), `*`(`^`(`+`(`/`(`*`(10, `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2))))), `/`(1, 2), tan(x)), 2))), `*`(`^`(`+`(`-`(`*`(`/`(1, 2), `*`(`^`(5, `/...
(8)
 

> restart;
int(sin(x)*arctan(sqrt(sec(x)-1)),x);
 

int(`*`(sin(x), `*`(arctan(`*`(`^`(`+`(sec(x), `-`(1)), `/`(1, 2)))))), x) (9)
 

> restart;
int(x^3*exp(1)^arcsin(x)/sqrt(1-x^2),x);
 

`+`(`*`(`/`(1, 10), `*`(`+`(x, `-`(`*`(3, `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))))), `*`(exp(arcsin(x)), `*`(`^`(x, 2))))), `*`(`/`(3, 10), `*`(exp(arcsin(x)), `*`(`+`(x, `-`(`*`(`^`(`+`(`-`... (10)
 

>
 

>