What is the integral of sqrt(x^5) ?

The integral of sqrt(x^5) is 2/7 x^{7/2}+C

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integral of sqrt(x^5)

\int x^{5} d x

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

Solution steps

\int x^{5} d x

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

assuming

x \geq 0

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

Apply the Power Rule

: \frac{2}{7} x^{\frac{7}{2}}

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

Add a constant to the solution

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

\int sec (t) (sec (t) - tan (t)) d t

\frac{d}{d x} (\frac{1}{f ( x ) ( x ) ^{- 1} ( x )})

d s = 2 s d t

n = 0 \sum \infty 5 (- \frac{1}{3})^{n}

x \to 4 lim (\frac{( x ^{2} - 16 )}{2 - x})