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Popular >

integral of (x^2)/2

Solution

integral

\frac{x ^{2}}{2}

Solution

\frac{x ^{3}}{6} + C

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int x^{2} d x

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{x ^{3}}{3}

Simplify

\frac{1}{2} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{6}

= \frac{x ^{3}}{6}

Add a constant to the solution

= \frac{x ^{3}}{6} + C

Popular Examples

integral of (sin^3(x))/(1+cos(x))

\int \frac{sin ^{3} ( x )}{1 + cos ( x )} d x

integral of e^{-0.05t}(100t^4+10t^3)

\int e^{- 0.05 t} (100 t^{4} + 10 t^{3}) d t

integral of (ln(x))^2 1/x

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

integral of (ln(ln(y)))/y

\int \frac{ln ( ln ( y ) )}{y} d y

integral of e^{(x^2)^{22}}x^2)^2

\int e^{(x^{2})^{22}} d (x^{2})^{2}

Frequently Asked Questions (FAQ)

What is the integral of (x^2)/2 ?
The integral of (x^2)/2 is (x^3)/6+C