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Single Variable Calculus

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Moderate

Integral with Trigonometric or Standard Substitution?

SVCALC-DGQEEG

Evaluate the indefinite integral:

$$\int \dfrac{x^5}{\sqrt{x^2+2}}dx$$

A

$\dfrac15 (x^2+2)^{\frac52}+\dfrac43(x^2+2)^{\frac32}+4 (x^2+2)^{\frac12} +C$

B

$\dfrac25 (x^2+2)^{\frac52}-\dfrac83(x^2+2)^{\frac32}+8 (x^2+2)^{\frac12} +C$

C

$\dfrac15 (x^2+2)^{\frac52}-\dfrac43(x^2+2)^{\frac32}+4 (x^2+2)^{\frac12} +C$

D

$\dfrac15 (x^2+2)^{\frac72}-\dfrac23(x^2+2)^{\frac52}+8 (x^2+2)^{\frac32} +C$