Find $\int x ^ { 4 } \sin \left( x ^ { 5 } \right) d x$
A) $\frac { 1 } { 5 } \sin \left( x ^ { 5 } \right) + C$
B) $\frac { 1 } { 5 } \cos \left( x ^ { 5 } \right) + C$
C) $\frac { - 1 } { 5 } \cos \left( x ^ { 5 } \right) + C$
D) $\frac { - 1 } { 5 } \sin \left( x ^ { 5 } \right) + C$

Question

Quizplus · Accepted Answer

This integral can be solved using a substitution method. Let $u = x^5$, then $du = 5x^4 dx$. Therefore, $dx = \frac{du}{5x^4}$, and the integral becomes $\int \sin(u) \frac{du}{5}$, which simplifies to $\frac{1}{5} \int \sin(u) du$. The integral of $\sin(u)$ is $-\cos(u)$, so the answer is $\frac{-1}{5} \cos(x^5) + C$.

Find ∫x4sin⁡(x5)dx\int x ^ { 4 } \sin \left( x ^ { 5 } \right) d x∫x4sin(x5)dx

Find $\int x ^ { 4 } \sin \left( x ^ { 5 } \right) d x$