How do you find the indefinite integral of $int (cosx)/(7sin(x)+42)dx$ ?

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Answer 1 · 2015-10-26T05:15:22

$1/7ln(sinx+6)$

Start by moving any constants outside of the integral. In this case we can pull out $1/7$ .

$1/7intcosx/(sinx+6)dx$

We can use substitution to simplify the integral.

$u=sinx+6->du=cosx dx$

Plugging $u$ and $du$ in the integral simplifies to;

$1/7int1/udu$

The integral of $1/x$ is $ln|x| +C$ .

$1/7ln|u|+C$

Undoing our earlier substitution, we get the solution to our integral.

$1/7ln|sinx+6|+C$

How do you find the indefinite integral of int (cosx)/(7sin(x)+42)dxint (cosx)/(7sin(x)+42)dx?