Find the indefinite integral of the following function. $\int 4 x ^ { 3 } \cos x ^ { 4 } d x$
A) $\cos x ^ { 4 } + C$
B) $\sin x ^ { 4 } + C$
C) $\sin x ^ { 3 }$
D) $\frac { \sin x ^ { 4 } } { 4 } + C$
E) $\sin x ^ { 4 }$

Question

Quizplus · Accepted Answer

This integral can be solved by recognizing it as a case for u-substitution. Let $u = x^4$, then $du = 4x^3 dx$. The integral becomes $\int \cos(u) du$, which is $\sin(u) + C$, or substituting back for $u$, $\sin(x^4) + C$.

Find the Indefinite Integral of the Following Function ∫4x3cos⁡x4dx\int 4 x ^ { 3 } \cos x ^ { 4 } d x∫4x3cosx4dx

Find the Indefinite Integral of the Following Function $\int 4 x ^ { 3 } \cos x ^ { 4 } d x$