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Popular >

integral of x/3

Solution

integral

\frac{x}{3}

Solution

\frac{x ^{2}}{6} + C

Solution steps

\int \frac{x}{3} d x

Take the constant out:

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

= \frac{1}{3} \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

= \frac{x ^{2}}{6}

Add a constant to the solution

= \frac{x ^{2}}{6} + C

Popular Examples

integral of sin(x^4)integral

sin (x^{4})

integral of 1/((1+y^2))integral

\frac{1}{( 1 + y ^{2} )}

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

\frac{1}{( 1 + 2 x ^{2} )}

integral of e^{-4}x integral

e^{- 4} x

integral of (4x)/((x^2+1))integral

\frac{4 x}{( x ^{2} + 1 )}

Frequently Asked Questions (FAQ)

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