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Popular >

integral of (1-x^2)x

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of (3x^2+2x-7)/(x^2-3x+2)

\int \frac{3 x ^{2} + 2 x - 7}{x ^{2} - 3 x + 2} d x

integral of (\sqrt[3]{x})/(sqrt(x)-1)

integral of 1/(3+cos^2(x))

\int \frac{1}{3 + cos ^{2} ( x )} d x

integral of pir^2

\int π r^{2} d r

integral of 1/(x^2+2x-1)

\int \frac{1}{x ^{2} + 2 x - 1} d x

Frequently Asked Questions (FAQ)

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