Find the indefinite integral $$\int \sqrt [ 13 ] { x ^ { 8 } } d x$$
A) $\frac { 8 } { 13 } x ^ { 21 } + C$
B) $\frac { 21 } { 13 } x ^ { 13 / 21 } + C$
C) $\frac { 8 } { 21 } x ^ { 8 / 21 } + C$
D) $\frac { 13 } { 8 } x ^ { 21 } + C$
E) $\frac { 13 } { 21 } x ^ { 21 / 13 } + C$

Question

Find the indefinite integral $$\int \sqrt [ 13 ] { x ^ { 8 } } d x$$ 
A) $\frac { 8 } { 13 } x ^ { 21 } + C$
B) $\frac { 21 } { 13 } x ^ { 13 / 21 } + C$
C) $\frac { 8 } { 21 } x ^ { 8 / 21 } + C$
D) $\frac { 13 } { 8 } x ^ { 21 } + C$
E) $\frac { 13 } { 21 } x ^ { 21 / 13 } + C$

Quizplus · Accepted Answer

The integral $\int \sqrt[13]{x^8} dx$ simplifies to $\int x^{8/13} dx$. Using the power rule for integration, $\int x^n dx = \frac{x^{n+1}}{n+1} + C$, we get $\frac{x^{(8/13)+1}}{(8/13)+1} + C = \frac{x^{21/13}}{21/13} + C$, which simplifies to $\frac{13}{21} x^{21/13} + C$.

Find the Indefinite Integral ∫x813dx\int \sqrt [ 13 ] { x ^ { 8 } } d x∫13x8​dx

Find the Indefinite Integral $\int \sqrt [ 13 ] { x ^ { 8 } } d x$