Question

Find the integral of sin(x) cos(x)/sin^2(x)-4 dx

Answer 1

sin(x) cos(x)/(sin^2(x)-4) =

-sin(x) cos(x)/(cos^2(x) + 3)

-sin(x) is the derivative of cos(x), therefore,

so d(cos(x)) = -sin(x) dx

Integral of

-sin(x) cos(x)/(cos^2(x) + 3) dx =

Integral of

cos(x)/(cos^2(x) + 3) dcos(x) =

Integral of u/(u^2+3) du =

1/2 Integral of 2u/(u^2+3) du =

1/2 Log(u^2+3) =

1/2 Log[cos^2(x) + 3]