Use a table of integrals to evaluate the integral. $$\int x ^ { 3 } \sin \left( x ^ { 2 } + 3 \right) d x$$
A) $\frac { 1 } { 2 } \sin \left( x ^ { 2 } + \sqrt { 3 } \right) - \frac { 1 } { 2 } x ^ { 2 } \cos \left( x ^ { 2 } + \sqrt { 3 } \right) + C$
B) $\frac { 1 } { 2 } \sin \left( x ^ { 2 } + 3 \right) - \frac { 1 } { 2 } x ^ { 2 } \cos \left( x ^ { 2 } + 3 \right) + C$
C) $- \frac { 1 } { 2 } \sin \left( x ^ { 2 } + \sqrt { 3 } \right) - \frac { 1 } { 2 } x ^ { 2 } \cos \left( x ^ { 2 } + \sqrt { 3 } \right) + C$
D) $- \frac { 1 } { 2 } \sin \left( x ^ { 2 } + 3 \right) - \frac { 1 } { 2 } x ^ { 2 } \cos \left( x ^ { 2 } + 3 \right) + C$

Question

Quizplus · Accepted Answer

The correct answer is B because the integral of $x ^ { 3 } \sin \left( x ^ { 2 } + 3 \right) d x$ is $\frac { 1 } { 2 } \sin \left( x ^ { 2 } + 3 \right) - \frac { 1 } { 2 } x ^ { 2 } \cos \left( x ^ { 2 } + 3 \right) + C$.

Use a Table of Integrals to Evaluate the Integral ∫x3sin⁡(x2+3)dx\int x ^ { 3 } \sin \left( x ^ { 2 } + 3 \right) d x∫x3sin(x2+3)dx

Use a Table of Integrals to Evaluate the Integral $\int x ^ { 3 } \sin \left( x ^ { 2 } + 3 \right) d x$