What is the integral of (8x+3)sqrt(4x^2+3x) ?

The integral of (8x+3)sqrt(4x^2+3x) is 2/3 (4x^2+3x)^{3/2}+C

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integral of (8x+3)sqrt(4x^2+3x)

\int (8 x + 3) 4 x^{2} + 3 x d x

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

Solution steps

\int (8 x + 3) 4 x^{2} + 3 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 = 4 x^{2} + 3 x

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{x ^{2} + 13 x + 36}{x ^{2} + 8 x - 9})

9 x^{\frac{2}{3}}

f (x) = 6 sec (x)

\frac{d}{d x} (\frac{ln ( x )}{x ^{4}})

\frac{d y}{d x} + y = e^{5 x}

What is the integral of (8x+3)sqrt(4x^2+3x) ?
The integral of (8x+3)sqrt(4x^2+3x) is 2/3 (4x^2+3x)^{3/2}+C