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Popular >

integral of xsqrt(x^2)

Solution

\int x x^{2} d x

Solution

\frac{x ^{3}}{3} + C

Solution steps

\int x x^{2} d x

x^{2} = (x),

assuming

x \geq 0

= \int xx d x

Simplify

xx : x^{2}

= \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{3}}{3} + C

Popular Examples

limit as x approaches 2 of 2x^2+5x+3

x \to 2 lim (2 x^{2} + 5 x + 3)

integral of 2x(x^2+6)^3

\int 2 x (x^{2} + 6)^{3} d x

integral of (\sqrt[10]{x}+\sqrt[11]{x})

integral of (sin^2(1/t))/(t^2)

\int \frac{sin ^{2} ( \frac{1}{t} )}{t ^{2}} d t

sum from n=0 to infinity of (-5x)^n

n = 0 \sum \infty (- 5 x)^{n}

Frequently Asked Questions (FAQ)

What is the integral of xsqrt(x^2) ?
The integral of xsqrt(x^2) is (x^3)/3+C