What is the integral of sqrt(x^7) ?

The integral of sqrt(x^7) is 2/9 x^{9/2}+C

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integral of sqrt(x^7)

\int x^{7} d x

\frac{2}{9} x^{\frac{9}{2}} + C

Solution steps

\int x^{7} d x

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

assuming

x \geq 0

= \int x^{\frac{7}{2}} d x

Apply the Power Rule

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

= \frac{2}{9} x^{\frac{9}{2}}

Add a constant to the solution

= \frac{2}{9} x^{\frac{9}{2}} + C

\frac{d}{d x} (\frac{1 - cos ( x )}{1 + cos ( x )})

\int \frac{1}{( 25 - y ^{2} ) - x ^{2}} d x

sin (2 t) + 2 cos (2 t) + e^{- t} sin (2 t)

y^{^{'}} = 3 y^{2}

n = 1 \sum \infty 8^{n} x^{n} n!