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Popular >

integral of x^3-2x^2

Solution

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

Solution

\frac{x ^{4}}{4} - \frac{2 x ^{3}}{3} + C

Solution steps

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

= \frac{x ^{4}}{4} - \frac{2 x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{2 x ^{3}}{3} + C

Popular Examples

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\int \frac{x}{( 2 x ^{2} + 1 ) ^{4}} d x

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\int x (1 - 2 x)^{99} d x

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\int x (sin (x) - 1) d x

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\int (\frac{5}{x} + \frac{x}{5}) d x

integral of (x^2+8)/(xsqrt(x^2-4))

\int \frac{x ^{2} + 8}{x x ^{2} - 4} d x

Frequently Asked Questions (FAQ)

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