$\int \frac{(2 \sin x + 5) \cos x}{\sin^{2} x + 5 \sin x} d x$

Answer

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Answer

$Math input error$

Steps

Step 1 ：Let $u = s i n x + 5$ , then $d u = c o s x d x$

Step 2 ：Substitute $u$ and $d u$ into the integral: $Math input error$

Step 3 ：Separate the integral: $Math input error$

Step 4 ：Simplify the integrals: $Math input error$

Step 5 ：Integrate: $Math input error$

Step 6 ：Substitute back $u = s i n x + 5$ : $Math input error$

Step 7 ： $Math input error$