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Popular >

integral of x(3x-2)

Solution

\int x (3 x - 2) d x

Solution

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

Solution steps

\int x (3 x - 2) d x

Expand

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

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

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of-x^2e^{2x^3}

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

integral of e^x+4pi-x^e

\int e^{x} + 4 π - x^{e} d x

integral of 1/3 sin(x)-1/4 cos(x)

\int \frac{1}{3} sin (x) - \frac{1}{4} cos (x) d x

integral of sqrt(z^2+1)

\int z^{2} + 1 d z

integral of 18xe^{3x^2}

\int 18 x e^{3 x^{2}} d x

Frequently Asked Questions (FAQ)

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