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Popular >

integral of 2x^3-2x

Solution

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

Solution

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

Solution steps

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

\int 2 x^{3} d x = \frac{x ^{4}}{2}

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

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

Add a constant to the solution

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

Popular Examples

integral of 1/(yx)

\int \frac{1}{y x} d x

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\int \frac{1}{( 4 + 9 x ^{2} ) ^{- \frac{3}{2}}} d x

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\int - \frac{13300}{( 5 x + 40 ) ^{2}} d x

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

integral of (x^5+2)/x

\int \frac{x ^{5} + 2}{x} d x

Frequently Asked Questions (FAQ)

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