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Popular Calculus >

integral of x 3/2

Solution

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

Solution

\frac{3 x ^{2}}{4} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

Simplify

\frac{3}{2} \cdot \frac{x ^{2}}{2} : \frac{3 x ^{2}}{4}

= \frac{3 x ^{2}}{4}

Add a constant to the solution

= \frac{3 x ^{2}}{4} + C

Graph

Popular Examples

integral of (6x^2)/((4x^3-9)^3)

\int \frac{6 x ^{2}}{( 4 x ^{3} - 9 ) ^{3}} d x

integral of sqrt(x^2+2x+2)

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

integral of 4/((4x-1)ln(4x-1))

\int \frac{4}{( 4 x - 1 ) ln ( 4 x - 1 )} d x

integral of (8x^3-6x^{-2})

\int (8 x^{3} - 6 x^{- 2}) d x

integral of (3x^2)/(x^3+5)

\int \frac{3 x ^{2}}{x ^{3} + 5} d x

Frequently Asked Questions (FAQ)

What is the integral of x 3/2 ?
The integral of x 3/2 is (3x^2)/4+C