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Popular >

integral of (x^2-1)x

Solution

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

Solution

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

Solution steps

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

Expand

(x^{2} - 1) x : x^{3} - x

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

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

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

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

Add a constant to the solution

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

Popular Examples

(\partial)/(\partial x)(-1-2x)

\frac{\partial}{\partial x} (- 1 - 2 x)

(e^{- t})^{^{'}}

derivative of-10e^{-x^2}x derivative of

- 10 e^{- x^{2}} x

y^{^{'}} = \frac{y + t ^{3}}{t}

integral from 1 to 2 of 7/(x^3+3x)

\int_{1}^{2} \frac{7}{x ^{3} + 3 x} d x

Frequently Asked Questions (FAQ)

What is the integral of (x^2-1)x ?
The integral of (x^2-1)x is (x^4)/4-(x^2)/2+C