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Popular >

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

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

= 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

Popular Examples

integral of x/(sqrt(81-x^2))

\int \frac{x}{81 - x ^{2}} d x

integral of yx^3e^{x^2y^2}

\int y x^{3} e^{x^{2} y^{2}} d y

integral of x^3e^{-x/c}

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

integral of (sqrt(x)+3x)

\int (x + 3 x) d x

integral of 5/((x-4)^2)

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