What is the integral of (2x+5)(x^2+5x)^7 ?

The integral of (2x+5)(x^2+5x)^7 is ((x^2+5x)^8)/8+C

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integral of (2x+5)(x^2+5x)^7

\int (2 x + 5) (x^{2} + 5 x)^{7} d x

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

Solution steps

\int (2 x + 5) (x^{2} + 5 x)^{7} d x

Apply u-substitution

: \int u^{7} d u

= \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= \frac{u ^{8}}{8}

Substitute back

u = x^{2} + 5 x

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

Add a constant to the solution

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

\frac{d y}{d x} = \frac{13 x y}{( ln ( y ) ) ^{10}}

\frac{d h}{d t} = - h, h (0) = 0

y^{^{'}} = \frac{5 y}{x + 3}

x \to - 7 lim (\frac{x ^{2} - 2}{7 - x})

\int (4 x - 1)^{2} d x

What is the integral of (2x+5)(x^2+5x)^7 ?
The integral of (2x+5)(x^2+5x)^7 is ((x^2+5x)^8)/8+C