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Popular >

integral of (2x)/3

Solution

\int \frac{2 x}{3} d x

Solution

\frac{x ^{2}}{3} + C

Solution steps

\int \frac{2 x}{3} d x

Take the constant out:

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

= \frac{2}{3} \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

= \frac{x ^{2}}{3} + C

Popular Examples

integral of (7x^2)/(sqrt(4x-x^2))

\int \frac{7 x ^{2}}{4 x - x ^{2}} d x

integral from 0 to 1 of xsqrt(3-x^2)

\int_{0}^{1} x 3 - x^{2} d x

tangent of f(x)=[1+e^x][ln(x)],\at x=1 tangent of

f (x) = [1 + e^{x}] [ln (x)], at x = 1

f (x) = e^{x} cos (x)

v^{''} - v = 0

Frequently Asked Questions (FAQ)

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