Evaluate the integral.
-$$\int x ^ { 5 } \sqrt { x ^ { 6 } + 8 } d x$$
A) $\frac { 1 } { 9 } \left( x ^ { 6 } + 8 \right) ^ { 3 / 2 } + C$
B) $- \frac { 1 } { 3 } \left( x ^ { 6 } + 8 \right) ^ { - 1 / 2 } + C$
C) $\frac { 2 } { 3 } \left( x ^ { 6 } + 8 \right) ^ { 3 / 2 } + C$
D) $4 \left( x ^ { 6 } + 8 \right) ^ { 3 / 2 } + C$

Question

Quizplus · Accepted Answer

To solve the integral $\int x^5 \sqrt{x^6 + 8} dx$, let $u = x^6 + 8$. Then, $du = 6x^5 dx$, and $\frac{1}{6}du = x^5 dx$. Substituting $u$ and $du$ into the integral gives $\frac{1}{6} \int \sqrt{u} du$, which simplifies to $\frac{1}{6} \cdot \frac{2}{3} u^{3/2} + C$, or $\frac{1}{9} (x^6 + 8)^{3/2} + C$.

Evaluate the Integral ∫x5x6+8dx\int x ^ { 5 } \sqrt { x ^ { 6 } + 8 } d x∫x5x6+8​dx

Evaluate the Integral $\int x ^ { 5 } \sqrt { x ^ { 6 } + 8 } d x$