Find the indefinite integral. $\int \frac { x ^ { 3 } } { 2 x ^ { 4 } + 1 } d x$
A) $\frac { 1 } { 8 } \ln \left| 2 x ^ { 4 } + 1 \right| + C$
B) $\frac { 1 } { 2 x ^ { 4 } + 1 } + C$
C) $\ln \left| 2 x ^ { 4 } - 1 \right| + C$
D) $\ln \left| 2 x ^ { 4 } + 1 \right| + C$
E) $\frac { 1 } { 16 } \ln \left| 2 x ^ { 4 } + 1 \right| + C$

Question

Quizplus · Accepted Answer

The integral can be solved by recognizing that the derivative of the denominator $2x^4 + 1$ is $8x^3$, which is a constant multiple of the numerator $x^3$. Therefore, the integral simplifies to $\frac{1}{8}\ln|2x^4 + 1| + C$, after adjusting for the constant multiple.

Find the Indefinite Integral ∫x32x4+1dx\int \frac { x ^ { 3 } } { 2 x ^ { 4 } + 1 } d x∫2x4+1x3​dx

Find the Indefinite Integral $\int \frac { x ^ { 3 } } { 2 x ^ { 4 } + 1 } d x$