Find the integral.
-$\int \frac{x^{5}}{x^{6}+7} d x$
A) $\frac{1}{5} \ln \left|x^{6}+7\right|+C$
B) $-\ln \left(x^{6}+7\right)+C$
C) $\frac{1}{6} \ln \left|x^{6}+7\right|+C$
D) $6 \ln \left|x^{6}+7\right|+C$

Question

Quizplus · Accepted Answer

The integral can be solved using substitution. Let $ u = x^6 + 7 $, then $ du = 6x^5 dx $. The integral becomes $\frac{1}{6} \int \frac{1}{u} du = \frac{1}{6} \ln |u| + C = \frac{1}{6} \ln |x^6 + 7| + C$.

Find the Integral ∫x5x6+7dx\int \frac{x^{5}}{x^{6}+7} d x∫x6+7x5​dx A) 15ln⁡∣x6+7∣+C\frac{1}{5} \ln \left|x^{6}+7\right|+C51​ln​x6+7​+C B) −ln⁡(x6+7)+C-\ln \left(x^{6}+7\right)+C−ln(x6+7)+C

Find the Integral $\int \frac{x^{5}}{x^{6}+7} d x$ A) $\frac{1}{5} \ln \left|x^{6}+7\right|+C$ B) $-\ln \left(x^{6}+7\right)+C$