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

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

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integral of (2+3x)x

\int (2 + 3 x) x d x

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

Solution steps

\int (2 + 3 x) x d x

Apply Integration By Parts

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

Expand

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

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

Add a constant to the solution

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

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