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Popular >

integral of x^2(2x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Simplify

x^{2} x : 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

Graph

Popular Examples

integral of x/(sqrt(16-x^4))

\int \frac{x}{16 - x ^{4}} d x

integral of (9x^2+1)ln(x)

\int (9 x^{2} + 1) ln (x) d x

integral of 5xe^{2x^2}

\int 5 x e^{2 x^{2}} d x

integral of sqrt((x^3-7)/(x^{11))}

\int \frac{x ^{3} - 7}{x ^{11}} d x

integral of (8x)/(sqrt(10x-x^2+11))

\int \frac{8 x}{10 x - x ^{2} + 11} d x

Frequently Asked Questions (FAQ)

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