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Popular Calculus >

integral of 2x*x^2

Solution

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

Solution

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

Solution steps

\int 2 x x^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Simplify

x x^{2} : x^{3}

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

Apply the Power Rule

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

Simplify

2 \cdot \frac{x ^{4}}{4} : \frac{x ^{4}}{2}

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

Add a constant to the solution

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

Graph

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\int x^{3} e^{- \frac{x}{c}} d x

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\int \frac{5}{( x - 4 ) ^{2}} d x

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\int \frac{6}{x} + 2 π d x

integral of 9/(5^2+x^2)

\int \frac{9}{5 ^{2} + x ^{2}} d x

integral of (x)(cos(x))

\int (x) (cos (x)) d x

Frequently Asked Questions (FAQ)

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