What is the integral of xsqrt(x-15) ?

The integral of xsqrt(x-15) is 2/5 (x-15)^{5/2}+10(x-15)^{3/2}+C

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integral of xsqrt(x-15)

\int x x - 15 d x

\frac{2}{5} (x - 15)^{\frac{5}{2}} + 10 (x - 15)^{\frac{3}{2}} + C

Solution steps

\int x x - 15 d x

Apply u-substitution

: \int (u + 15) u d u

= \int (u + 15) u d u

Expand

(u + 15) u : u^{\frac{3}{2}} + 15 u

= \int u^{\frac{3}{2}} + 15 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 15 u d u

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

\int 15 u d u = 10 u^{\frac{3}{2}}

= \frac{2}{5} u^{\frac{5}{2}} + 10 u^{\frac{3}{2}}

Substitute back

u = x - 15

= \frac{2}{5} (x - 15)^{\frac{5}{2}} + 10 (x - 15)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{5} (x - 15)^{\frac{5}{2}} + 10 (x - 15)^{\frac{3}{2}} + C

\int x e^{x y} d y

\int e^{x + 1} d x

\frac{d}{d x} (\frac{2}{x ^{2} + 4})

f (t) = t^{3} e^{- 2 t} cos (6 t)

\frac{\partial}{\partial x} (\frac{( x ^{2} + y ^{2} - 4 )}{x y})

What is the integral of xsqrt(x-15) ?
The integral of xsqrt(x-15) is 2/5 (x-15)^{5/2}+10(x-15)^{3/2}+C