What is the integral of xsqrt(x-10) ?

The integral of xsqrt(x-10) is 2/5 (x-10)^{5/2}+20/3 (x-10)^{3/2}+C

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integral of xsqrt(x-10)

\int x x - 10 d x

\frac{2}{5} (x - 10)^{\frac{5}{2}} + \frac{20}{3} (x - 10)^{\frac{3}{2}} + C

Solution steps

\int x x - 10 d x

Apply u-substitution

: \int (u + 10) u d u

= \int (u + 10) u d u

Expand

(u + 10) u : u^{\frac{3}{2}} + 10 u

= \int u^{\frac{3}{2}} + 10 u d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{\frac{3}{2}} d u + \int 10 u d u

\int u^{\frac{3}{2}} d u = \frac{2}{5} u^{\frac{5}{2}}

\int 10 u d u = \frac{20}{3} u^{\frac{3}{2}}

= \frac{2}{5} u^{\frac{5}{2}} + \frac{20}{3} u^{\frac{3}{2}}

Substitute back

u = x - 10

= \frac{2}{5} (x - 10)^{\frac{5}{2}} + \frac{20}{3} (x - 10)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{5} (x - 10)^{\frac{5}{2}} + \frac{20}{3} (x - 10)^{\frac{3}{2}} + C

\frac{3}{s} + \frac{16}{s ( s + 1 )}

\int_{1}^{e^{2}} \frac{ln ( x )}{x ^{2}} d x

\frac{\partial}{\partial x} (\frac{a - b ^{2}}{x - c ^{2}})

\frac{d}{d x} (5 - \frac{4}{x})

\frac{- u ^{2} + 7}{( u ^{2} + 7 ) ^{2}}

What is the integral of xsqrt(x-10) ?
The integral of xsqrt(x-10) is 2/5 (x-10)^{5/2}+20/3 (x-10)^{3/2}+C