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Popular >

integral of x(x^2+2)

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of tsqrt(4+9t^2)

\int t 4 + 9 t^{2} d t

integral of 1/(1+64x^2)

\int \frac{1}{1 + 64 x ^{2}} d x

integral from 0 to infinity of te^{-t^2}

\int_{0}^{\infty} t e^{- t^{2}} d t

derivative of x/(x-9)

\frac{d}{d x} (\frac{x}{x - 9})

integral of (3x-5)^{1/2}

\int (3 x - 5)^{\frac{1}{2}} d x

Frequently Asked Questions (FAQ)

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