What is the integral of x(x^2+9)^3 ?

The integral of x(x^2+9)^3 is 1/8 (x^2+9)^4+C

Popular >

integral of x(x^2+9)^3

\int x (x^{2} + 9)^{3} d x

\frac{1}{8} (x^{2} + 9)^{4} + C

Solution steps

\int x (x^{2} + 9)^{3} d x

Apply u-substitution

: \int \frac{u ^{3}}{2} d u

= \int \frac{u ^{3}}{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^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{1}{2} \cdot \frac{u ^{4}}{4}

Substitute back

u = x^{2} + 9

= \frac{1}{2} \cdot \frac{( x ^{2} + 9 ) ^{4}}{4}

Simplify

\frac{1}{2} \cdot \frac{( x ^{2} + 9 ) ^{4}}{4} : \frac{1}{8} (x^{2} + 9)^{4}

= \frac{1}{8} (x^{2} + 9)^{4}

Add a constant to the solution

= \frac{1}{8} (x^{2} + 9)^{4} + C

\int \frac{x}{x ^{3} + 3 x ^{2} + 7 x + 5} d x

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

\int (3 x^{2} + \frac{25}{2 x ^{3}}) d x

\int (4 w - 3)^{3} d w

\int \frac{10 ln ( x )}{x} d x

What is the integral of x(x^2+9)^3 ?
The integral of x(x^2+9)^3 is 1/8 (x^2+9)^4+C