What is the integral of (10x+4)sqrt(5x^2+4x) ?

The integral of (10x+4)sqrt(5x^2+4x) is 2/3 (5x^2+4x)^{3/2}+C

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integral of (10x+4)sqrt(5x^2+4x)

\int (10 x + 4) 5 x^{2} + 4 x d x

\frac{2}{3} (5 x^{2} + 4 x)^{\frac{3}{2}} + C

Solution steps

\int (10 x + 4) 5 x^{2} + 4 x d x

Apply u-substitution

= \int u d u

Apply the Power Rule

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

Substitute back

u = 5 x^{2} + 4 x

= \frac{2}{3} (5 x^{2} + 4 x)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (5 x^{2} + 4 x)^{\frac{3}{2}} + C

What is the integral of (10x+4)sqrt(5x^2+4x) ?
The integral of (10x+4)sqrt(5x^2+4x) is 2/3 (5x^2+4x)^{3/2}+C