Find the indefinite integral. $\int \frac { x ^ { 2 } } { 3 x ^ { 3 } + 10 } d x$
A) $\frac { 1 } { 9 } \ln \left| 3 x ^ { 3 } + 10 \right| + C$
B) $\ln \left| 3 x ^ { 3 } + 10 \right| + C$
C) $\frac { x ^ { 3 } } { 3 x ^ { 4 } + 10 x } + C$
D)integral does not exist
E)none of the above

Question

Quizplus · Accepted Answer

The integral can be simplified by recognizing that the derivative of the denominator $3x^3 + 10$ is $9x^2$, which is closely related to the numerator $x^2$. By substituting $u = 3x^3 + 10$, we find that $du = 9x^2 dx$, which simplifies the integral to $\frac{1}{3}\int \frac{1}{u} du$, leading to $\frac{1}{3} \ln|u| + C$, or $\frac{1}{9} \ln|3x^3 + 10| + C$.

Find the Indefinite Integral ∫x23x3+10dx\int \frac { x ^ { 2 } } { 3 x ^ { 3 } + 10 } d x∫3x3+10x2​dx

Find the Indefinite Integral $\int \frac { x ^ { 2 } } { 3 x ^ { 3 } + 10 } d x$