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Popular >

integral of 5x^{3/2}

Solution

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

Solution

2 x^{\frac{5}{2}} + C

Solution steps

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

Take the constant out:

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

= 5 \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

: \frac{2}{5} x^{\frac{5}{2}}

= 5 \cdot \frac{2}{5} x^{\frac{5}{2}}

Simplify

5 \cdot \frac{2}{5} x^{\frac{5}{2}} : 2 x^{\frac{5}{2}}

= 2 x^{\frac{5}{2}}

Add a constant to the solution

= 2 x^{\frac{5}{2}} + C

Graph

Popular Examples

limit as x approaches infinity of (x)(e^{1/x})

x \to \infty lim ((x) (e^{\frac{1}{x}}))

limit as t approaches 1 of sqrt(t+4)

t \to 1 lim (t + 4)

limit as x approaches 5 of-(x-3)^2

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

d/(dt)(1.1t+6.3t^3)

\frac{d}{d t} (1.1 t + 6.3 t^{3})

limit as x approaches infinity of ((x+1}{x+2})^{\frac{-4x)/5}

x \to \infty lim ((\frac{x + 1}{x + 2})^{\frac{- 4 x}{5}})

Frequently Asked Questions (FAQ)

What is the integral of 5x^{3/2} ?
The integral of 5x^{3/2} is 2x^{5/2}+C