What is the integral of (2x^2+4)^8*x ?

The integral of (2x^2+4)^8*x is 1/36 (2x^2+4)^9+C

Popular >

integral of (2x^2+4)^8*x

\int (2 x^{2} + 4)^{8} \cdot x d x

\frac{1}{36} (2 x^{2} + 4)^{9} + C

Solution steps

\int (2 x^{2} + 4)^{8} x d x

Apply u-substitution

: \int \frac{u ^{8}}{4} d u

= \int \frac{u ^{8}}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int u^{8} d u

Apply the Power Rule

: \frac{u ^{9}}{9}

= \frac{1}{4} \cdot \frac{u ^{9}}{9}

Substitute back

u = 2 x^{2} + 4

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

Simplify

\frac{1}{4} \cdot \frac{( 2 x ^{2} + 4 ) ^{9}}{9} : \frac{1}{36} (2 x^{2} + 4)^{9}

= \frac{1}{36} (2 x^{2} + 4)^{9}

Add a constant to the solution

= \frac{1}{36} (2 x^{2} + 4)^{9} + C

\int \frac{sin ( 3 x )}{e ^{x}} d x

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

\int - \frac{1100}{x ^{2}} d x

\int 1 + x^{4} + 2 x^{2} d x

\int \frac{5}{( 3 x - 1 ) ^{2}} d x

What is the integral of (2x^2+4)^8*x ?
The integral of (2x^2+4)^8*x is 1/36 (2x^2+4)^9+C