What is the integral of x(x^2+8)^5 ?

The integral of x(x^2+8)^5 is 1/12 (x^2+8)^6+C

Popular >

integral of x(x^2+8)^5

\int x (x^{2} + 8)^{5} d x

\frac{1}{12} (x^{2} + 8)^{6} + C

Solution steps

\int x (x^{2} + 8)^{5} d x

Apply u-substitution

: \int \frac{u ^{5}}{2} d u

= \int \frac{u ^{5}}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{1}{2} \cdot \frac{u ^{6}}{6}

Substitute back

u = x^{2} + 8

= \frac{1}{2} \cdot \frac{( x ^{2} + 8 ) ^{6}}{6}

Simplify

\frac{1}{2} \cdot \frac{( x ^{2} + 8 ) ^{6}}{6} : \frac{1}{12} (x^{2} + 8)^{6}

= \frac{1}{12} (x^{2} + 8)^{6}

Add a constant to the solution

= \frac{1}{12} (x^{2} + 8)^{6} + C

\int 4 x (2 x - 1) (4 x + 1) d x

\int \frac{x ^{3}}{3 1 + x ^{4}} d x

\int \frac{1}{x ( 4 - x ^{2} )} d x

\int \frac{7 x ^{2} - 2}{x ^{2}} d x

\int \frac{1}{2} + \frac{cos ( 2 x )}{2} d x

What is the integral of x(x^2+8)^5 ?
The integral of x(x^2+8)^5 is 1/12 (x^2+8)^6+C