# Math Help - indeifinit integrals

1. ## indeifinit integrals

Find the indefinite integral.

∫ (cos t) dt / (1 + sin t)

ln (1 + sin t) + C

But i can't figure out the steps.

2. Originally Posted by corinna
Find the indefinite integral.

∫ (cos t) dt / (1 + sin t)

ln (1 + sin t) + C

But i can't figure out the steps.
Recognise that the numerator is the derivative of the denominator. Hence substituting u for the denominator would work:

$u = 1 + \sin(t)$

$\frac{du}{dt} = \cos(t)$

$du = \cos(t)dt$

Hence integral becomes:

$\int \frac{du}{u}$