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Popular >

integral of x^2(1+x)

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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

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

= \frac{x ^{3}}{3} + \frac{x ^{4}}{4}

Add a constant to the solution

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

Popular Examples

integral of sqrt(49-9x^2)

\int 49 - 9 x^{2} d x

integral of 1/(sqrt(e^x-4))

\int \frac{1}{e ^{x} - 4} d x

integral of 1/(36+25x^2)

\int \frac{1}{36 + 25 x ^{2}} d x

integral of 1/(4-3cos^2(x)+5sin^2(x))

\int \frac{1}{4 - 3 cos ^{2} ( x ) + 5 sin ^{2} ( x )} d x

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

\int \frac{1 + 2 x}{1 - 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^3)/3+(x^4)/4+C