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Popular >

integral of x(2x-3)

Solution

\int x (2 x - 3) d x

Solution

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

Solution steps

\int x (2 x - 3) d x

Expand

x (2 x - 3) : 2 x^{2} - 3 x

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

Add a constant to the solution

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

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Frequently Asked Questions (FAQ)

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