What is the integral of (8x^2+5)^{10}x ?

The integral of (8x^2+5)^{10}x is 1/176 (8x^2+5)^{11}+C

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integral of (8x^2+5)^{10}x

\int (8 x^{2} + 5)^{10} x d x

\frac{1}{176} (8 x^{2} + 5)^{11} + C

Solution steps

\int (8 x^{2} + 5)^{10} x d x

Apply u-substitution

: \int \frac{u ^{10}}{16} d u

= \int \frac{u ^{10}}{16} d u

Take the constant out:

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

= \frac{1}{16} \cdot \int u^{10} d u

Apply the Power Rule

: \frac{u ^{11}}{11}

= \frac{1}{16} \cdot \frac{u ^{11}}{11}

Substitute back

u = 8 x^{2} + 5

= \frac{1}{16} \cdot \frac{( 8 x ^{2} + 5 ) ^{11}}{11}

Simplify

\frac{1}{16} \cdot \frac{( 8 x ^{2} + 5 ) ^{11}}{11} : \frac{1}{176} (8 x^{2} + 5)^{11}

= \frac{1}{176} (8 x^{2} + 5)^{11}

Add a constant to the solution

= \frac{1}{176} (8 x^{2} + 5)^{11} + C

\int 2 x (x^{2} + 7)^{7} d x

\frac{d y}{d x} = - \frac{1}{3} x^{3}

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

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

8 x^{2} y^{^{'}} = y^{^{'}} + 8 x e^{- y}

What is the integral of (8x^2+5)^{10}x ?
The integral of (8x^2+5)^{10}x is 1/176 (8x^2+5)^{11}+C