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

The integral of x(3x+2) is 3/2 x^3+x^2-(x^3)/2+C

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integral of x(3x+2)

\int x (3 x + 2) d x

\frac{3}{2} x^{3} + x^{2} - \frac{x ^{3}}{2} + C

Solution steps

\int x (3 x + 2) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} (3 x + 2) - \int \frac{3 x ^{2}}{2} d x

= \frac{1}{2} x^{2} (3 x + 2) - \int \frac{3 x ^{2}}{2} d x

\int \frac{3 x ^{2}}{2} d x = \frac{x ^{3}}{2}

= \frac{1}{2} x^{2} (3 x + 2) - \frac{x ^{3}}{2}

Expand

\frac{1}{2} x^{2} (3 x + 2) : \frac{3}{2} x^{3} + x^{2}

= \frac{3}{2} x^{3} + x^{2} - \frac{x ^{3}}{2}

Add a constant to the solution

= \frac{3}{2} x^{3} + x^{2} - \frac{x ^{3}}{2} + C

\int x sinh (x) d x

\int_{0}^{1} 6 (1 + x)^{5} d x

\frac{d}{d x} ((4 x)^{2})

\frac{\partial}{\partial z} (x^{2} + 3 yz + 4 x y)

n = 0 \sum \infty 6 (0.4)^{n}

What is the integral of x(3x+2) ?
The integral of x(3x+2) is 3/2 x^3+x^2-(x^3)/2+C