How do you find the indefinite integral of $\int \frac{cos t}{1 + sin t}$ $int cost/(1+sint)$ ?

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Answer 1 · 2017-02-08T04:49:08

$ln | sin t + t | + C$ $ln|sint + t| + C$

Let $u = sin t + 1$ $u = sint + 1$ . Then $d u = cos t d t$ $du = cos t dt$ and $d t = \frac{d u}{cos t}$ $dt = (du)/cost$ .

$\Rightarrow \int \frac{cos t}{u} \cdot \frac{d u}{cos t}$ $=>int cost/u * (du)/cost$

$\Rightarrow \int \frac{1}{u} d u$ $=>int 1/u du$

$\Rightarrow ln | u | + C$ $=>ln|u| + C$

$\Rightarrow ln | sin t + t | + C$ $=>ln|sint + t| + C$

Hopefully this helps!

How do you find the indefinite integral of ∫cost1+sintint cost/(1+sint)?