What is the integral of (10x+1)sqrt(5x^2+x) ?

The integral of (10x+1)sqrt(5x^2+x) is 2/3 (5x^2+x)^{3/2}+C

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integral of (10x+1)sqrt(5x^2+x)

\int (10 x + 1) 5 x^{2} + x d x

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

Solution steps

\int (10 x + 1) 5 x^{2} + 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 = 5 x^{2} + x

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

Add a constant to the solution

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

\int x e^{- y} d y

\frac{d}{d x} (x^{4} - 5 x)

\frac{e ^{- 2 s}}{s ^{4}}

\int \frac{12 x - 2}{6 x ^{2} - 2 x} d x

\frac{d}{d x} ((x^{3} + 3) (x + 2))

What is the integral of (10x+1)sqrt(5x^2+x) ?
The integral of (10x+1)sqrt(5x^2+x) is 2/3 (5x^2+x)^{3/2}+C