What is the integral of (8x^7+9)sqrt(x^8+9x) ?

The integral of (8x^7+9)sqrt(x^8+9x) is 2/3 (x^8+9x)^{3/2}+C

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integral of (8x^7+9)sqrt(x^8+9x)

\int (8 x^{7} + 9) x^{8} + 9 x d x

\frac{2}{3} (x^{8} + 9 x)^{\frac{3}{2}} + C

Solution steps

\int (8 x^{7} + 9) x^{8} + 9 x d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = x^{8} + 9 x

= \frac{2}{3} (x^{8} + 9 x)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (x^{8} + 9 x)^{\frac{3}{2}} + C

y = \frac{8}{x ^{2}}

\frac{d}{d x} (16 e^{2 x})

y = 3 arccos (\frac{x}{2})

\frac{d y}{d x} = \frac{4 sec ( y )}{( x + 5 ) ^{2}}

(- 2.8) (- 22.8)

What is the integral of (8x^7+9)sqrt(x^8+9x) ?
The integral of (8x^7+9)sqrt(x^8+9x) is 2/3 (x^8+9x)^{3/2}+C