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

The integral of 3x^{3/2} is 6/5 x^{5/2}+C

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integral of 3x^{3/2}

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

\frac{6}{5} x^{\frac{5}{2}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

3 \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{6}{5} x^{\frac{5}{2}}

= \frac{6}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{6}{5} x^{\frac{5}{2}} + C

\int \frac{sin ( 2 x )}{36 + cos ^{2} ( x )} d x

0.5 q^{^{''}} + 10 q^{^{'}} + 100 q = 150

\int_{0}^{\infty} 3 e^{- x} d x

12 t

30 x - 3 x