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

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

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

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

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

Solution steps

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

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

Add a constant to the solution

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

y^{^{'}} = e^{y} \cdot 5^{x}

x \to 0 lim (\frac{e ^{x}}{x})

\frac{\partial}{\partial x} (- 4 y^{2} x (6 - x^{2} y^{2}))

(x^{2} + 1) \cdot \frac{d y}{d x} + 3 x (y - 1) = 0

x \to 5 lim (3 x + 2)

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