What is the integral of (16x+5)sqrt(8x^2+5x) ?

The integral of (16x+5)sqrt(8x^2+5x) is 2/3 (8x^2+5x)^{3/2}+C

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integral of (16x+5)sqrt(8x^2+5x)

\int (16 x + 5) 8 x^{2} + 5 x d x

\frac{2}{3} (8 x^{2} + 5 x)^{\frac{3}{2}} + C

Solution steps

\int (16 x + 5) 8 x^{2} + 5 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 = 8 x^{2} + 5 x

= \frac{2}{3} (8 x^{2} + 5 x)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (8 x^{2} + 5 x)^{\frac{3}{2}} + C

\int x d (arcsin (x)) d x

\int x sin (\frac{x}{5}) d x

\int (3 x^{2} + 5 x) d x

\int \frac{( 1 - cos ( x ) )}{1 + cos ( x )} d x

\int (1 + tan (x))^{2} sec^{2} (x) d x

What is the integral of (16x+5)sqrt(8x^2+5x) ?
The integral of (16x+5)sqrt(8x^2+5x) is 2/3 (8x^2+5x)^{3/2}+C