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

The integral of 3x^{5/2} is 6/7 x^{7/2}+C

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integral of 3x^{5/2}

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

\frac{6}{7} x^{\frac{7}{2}} + C

Solution steps

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

Apply the Power Rule

= 3 \cdot \frac{2}{7} x^{\frac{7}{2}}

Simplify

3 \cdot \frac{2}{7} x^{\frac{7}{2}} : \frac{6}{7} x^{\frac{7}{2}}

= \frac{6}{7} x^{\frac{7}{2}}

Add a constant to the solution

= \frac{6}{7} x^{\frac{7}{2}} + C