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Popular Calculus >

integral of x(2+x^2)

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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