What is the integral from 2 to 5 of xsqrt(x-1) ?

The integral from 2 to 5 of xsqrt(x-1) is 256/15

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integral from 2 to 5 of xsqrt(x-1)

\int_{2}^{5} x x - 1 d x

\frac{256}{15}

Decimal

17.06666 \dots

Solution steps

\int_{2}^{5} x x - 1 d x

Apply u-substitution

: \int_{1}^{4} (u + 1) u d u

= \int_{1}^{4} (u + 1) u d u

Expand

(u + 1) u : u^{\frac{3}{2}} + u

= \int_{1}^{4} u^{\frac{3}{2}} + 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_{1}^{4} u^{\frac{3}{2}} d u + \int_{1}^{4} u d u

\int_{1}^{4} u^{\frac{3}{2}} d u = \frac{62}{5}

\int_{1}^{4} u d u = \frac{14}{3}

= \frac{62}{5} + \frac{14}{3}

Simplify

\frac{62}{5} + \frac{14}{3} : \frac{256}{15}

= \frac{256}{15}

y = \frac{t}{4 t - 5}

y^{^{''}} + y^{^{'}} + y = sin^{2} (x)

x \to 1 - lim (\frac{3}{x ^{2} - 1})

y = - x^{2} + 5 x - 3, y = x^{2} - 3 x + 3

\frac{\partial}{\partial y} (e^{y - x})

What is the integral from 2 to 5 of xsqrt(x-1) ?
The integral from 2 to 5 of xsqrt(x-1) is 256/15