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

The integral of 2x(x^2+5)^8 is 1/9 (x^2+5)^9+C

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

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

\frac{1}{9} (x^{2} + 5)^{9} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

= 2 \cdot \int \frac{u ^{8}}{2} d u

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int u^{8} d u

Apply the Power Rule

= 2 \cdot \frac{1}{2} \cdot \frac{u ^{9}}{9}

Substitute back

u = x^{2} + 5

= 2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 5 ) ^{9}}{9}

Simplify

2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 5 ) ^{9}}{9} : \frac{1}{9} (x^{2} + 5)^{9}

= \frac{1}{9} (x^{2} + 5)^{9}

Add a constant to the solution

= \frac{1}{9} (x^{2} + 5)^{9} + C

\int 11 x d x

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

\frac{d y}{d t} + e^{t} y = - 2 e^{t}

\frac{d}{d q} (- 0.1 q^{2} + 1.2 q + 46.4)

n = 1 \sum \infty (\frac{9}{8})^{n}

What is the integral of 2x(x^2+5)^8 ?
The integral of 2x(x^2+5)^8 is 1/9 (x^2+5)^9+C