Find the integral.
-$\int \frac{x^{4}}{5 x^{5}+3} d x$
A) $\frac{1}{5} \ln \left|5 x^{5}+3\right|+C$
B) $25 \ln \left(5 x^{5}+3\right)+C$
C) $\frac{1}{25} \ln \left|5 x^{5}+3\right|+C$
D) $25 \ln \left|5 x^{5}+3\right|+C$

Question

Quizplus · Accepted Answer

The integral can be solved using substitution. Let $ u = 5x^5 + 3 $, then $ du = 25x^4 dx $. The integral becomes $\frac{1}{25} \int \frac{1}{u} du = \frac{1}{25} \ln |u| + C = \frac{1}{25} \ln |5x^5 + 3| + C$.

Find the Integral ∫x45x5+3dx\int \frac{x^{4}}{5 x^{5}+3} d x∫5x5+3x4​dx A) 15ln⁡∣5x5+3∣+C\frac{1}{5} \ln \left|5 x^{5}+3\right|+C51​ln​5x5+3​+C

Find the Integral $\int \frac{x^{4}}{5 x^{5}+3} d x$ A) $\frac{1}{5} \ln \left|5 x^{5}+3\right|+C$