Evaluate the integral.
$\int 5 ^ { \sin \theta } \cos \theta d \theta$
A) $\frac { 5 ^ { \cos \theta } } { \ln ( 5 ) } + C$
B)
$\frac { 5 ^ { \sin \theta } } { \ln ( \sin \theta ) } + C$
C) $\frac { 5 ^ { \sin \theta } } { \ln ( 5 ) } + C$
D) $\frac { 5 ^ { \cos \theta } } { \ln ( \sin \theta ) }$
E) none of these

Question

Quizplus · Accepted Answer

This integral can be solved with the substitution $u = \sin(	heta), du = \cos(	heta) d	heta$. Thus,
\begin{align*}
\int 5^{\sin	heta}\cos	heta \, d	heta &= \int 5^u \, du \
&= \frac{5^u}{\ln(5)} + C \
&= \frac{5^{\sin	heta}}{\ln(5)} + C.
\end{align*}
Therefore, the answer is (C).

Evaluate the Integral ∫5sin⁡θcos⁡θdθ\int 5 ^ { \sin \theta } \cos \theta d \theta∫5sinθcosθdθ

Evaluate the Integral $\int 5 ^ { \sin \theta } \cos \theta d \theta$