What is the integral from 1 to 5 of (2x-1)^{5/2} ?

The integral from 1 to 5 of (2x-1)^{5/2} is 2186/7

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integral from 1 to 5 of (2x-1)^{5/2}

\int_{1}^{5} (2 x - 1)^{\frac{5}{2}} d x

\frac{2186}{7}

Decimal Notation

312.28571 \dots

Solution steps

\int_{1}^{5} (2 x - 1)^{\frac{5}{2}} d x

Apply u-substitution

: \int_{1}^{9} \frac{u ^{\frac{5}{2}}}{2} d u

= \int_{1}^{9} \frac{u ^{\frac{5}{2}}}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{1}^{9} u^{\frac{5}{2}} d u

Apply the Power Rule

: [\frac{2}{7} u^{\frac{7}{2}}]_{1}^{9}

= \frac{1}{2} [\frac{2}{7} u^{\frac{7}{2}}]_{1}^{9}

Compute the boundaries:

\frac{4372}{7}

= \frac{1}{2} \cdot \frac{4372}{7}

Simplify

= \frac{2186}{7}

\int 15 x e^{x^{2}} d x

\frac{d}{d x} (ln (\frac{2 x}{x + 9}))

x \to 0 - lim (x + 1)

b

sin (x), cos (x), 0, π

What is the integral from 1 to 5 of (2x-1)^{5/2} ?
The integral from 1 to 5 of (2x-1)^{5/2} is 2186/7