What is the integral of 20x^{3/2} ?

The integral of 20x^{3/2} is 8x^{5/2}+C

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integral of 20x^{3/2}

\int 20 x^{\frac{3}{2}} d x

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

Solution steps

\int 20 x^{\frac{3}{2}} d x

Take the constant out:

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

= 20 \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

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

= 20 \cdot \frac{2}{5} x^{\frac{5}{2}}

Simplify

20 \cdot \frac{2}{5} x^{\frac{5}{2}} : 8 x^{\frac{5}{2}}

= 8 x^{\frac{5}{2}}

Add a constant to the solution

= 8 x^{\frac{5}{2}} + C

\frac{2}{2 s - 1}

\frac{d}{d x} (5^{- \frac{x}{2}})

2 \cdot x

x \to 8 lim (7 (8 x + 5)^{3})

\int_{1}^{3} 3 d x