What is the integral of 8u^{7/2} ?

The integral of 8u^{7/2} is 16/9 u^{9/2}+C

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integral of 8u^{7/2}

\int 8 u^{\frac{7}{2}} d u

\frac{16}{9} u^{\frac{9}{2}} + C

Solution steps

\int 8 u^{\frac{7}{2}} d u

Take the constant out:

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

= 8 \cdot \int u^{\frac{7}{2}} d u

Apply the Power Rule

: \frac{2}{9} u^{\frac{9}{2}}

= 8 \cdot \frac{2}{9} u^{\frac{9}{2}}

Simplify

8 \cdot \frac{2}{9} u^{\frac{9}{2}} : \frac{16}{9} u^{\frac{9}{2}}

= \frac{16}{9} u^{\frac{9}{2}}

Add a constant to the solution

= \frac{16}{9} u^{\frac{9}{2}} + C

5^{x}, 0

y = (x^{4} + 2)^{2} (x^{5} + 4)^{4}

\frac{d}{d x} (e^{4} x^{7})

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

f (x) = x^{2} + 5