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Popular >

integral of x+x^2

Solution

\int x + x^{2} d x

Solution

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

Solution steps

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

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

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

= \frac{x ^{2}}{2} + \frac{x ^{3}}{3}

Add a constant to the solution

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

Popular Examples

integral of 5x^3

\int 5 x^{3} d x

derivative of (1+sin(x)cos(2x))

\frac{d}{d x} ((1 + sin (x)) cos (2 x))

sum from n=0 to infinity of (5n)/(2n-1)

n = 0 \sum \infty \frac{5 n}{2 n - 1}

y^{^{'}} + 3 y = e^{- 3 x}

integral from 2 to 3 of (4+2x)^2

\int_{2}^{3} (4 + 2 x)^{2} d x

Frequently Asked Questions (FAQ)

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