Evaluate the integral.
-$$\int \frac { \cos x d x } { 1 + 4 \sin x }$$
A) $4 \ln | 1 + 4 \sin x | + C$
B) $\ln | 1 + 4 \sin x | + C$
C) $\frac { 1 } { 4 } \ln | 1 + 4 \sin x | + C$
D) $4 \sin x + C$

Question

Quizplus · Accepted Answer

We can start by making a substitution $u=1+4\sin x$:
\begin{align*}
\int \frac{\cos x}{1+4\sin x}dx &=\frac{1}{4}\int \frac{d(1+4\sin x)}{1+4\sin x}\cdot\cos x\
&=\frac{1}{4}\ln|1+4\sin x|+C
\end{align*}
Therefore, the answer is C.

Evaluate the Integral ∫cos⁡xdx1+4sin⁡x\int \frac { \cos x d x } { 1 + 4 \sin x }∫1+4sinxcosxdx​

Evaluate the Integral $\int \frac { \cos x d x } { 1 + 4 \sin x }$