Integration using inverse trig indentities?

[Cpt Qwark]

Homework Statement

1.\int{\frac{sinx}{1+cos^{2}x}} \, dx
2.\int{\frac{1}{13-4x+x^2}} \, dx

Homework Equations

Inverse trig identities.

The Attempt at a Solution

For the first one, I'm not too sure about what to do with the sinx on the numerator and i have tried u-substitution to no avail (different answer). For the second one, I tried factorising but only had solutions for x\inℂ.

 

[eple]

You can maybe try to start with the substitution u = cos(x) and reforming the integral. A second substitution will be necessary after the first substitution.

 

[Raghav Gupta]

You can maybe try to start with the substitution u = cos(x) and reforming the integral. A second substitution will be necessary after the first substitution.

Second substitution is not necessary. It can be done in that first one.

 

[HallsofIvy]

For the second integral start by completing the square in the denominator.