What is the integral of (1-x)^{3/2} ?

The integral of (1-x)^{3/2} is -2/5 (1-x)^{5/2}+C

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integral of (1-x)^{3/2}

\int (1 - x)^{\frac{3}{2}} d x

- \frac{2}{5} (1 - x)^{\frac{5}{2}} + C

Solution steps

\int (1 - x)^{\frac{3}{2}} d x

Apply u-substitution

: \int - u^{\frac{3}{2}} d u

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{2}{5} u^{\frac{5}{2}}

= - \frac{2}{5} u^{\frac{5}{2}}

Substitute back

u = 1 - x

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

Add a constant to the solution

= - \frac{2}{5} (1 - x)^{\frac{5}{2}} + C

sec^{5} (x)

\int_{1200}^{1210} x \cdot 0.1 d x

(\frac{4 x ^{3} + 5}{- 5 x ^{2} + 1})^{\frac{1}{4}}

\frac{x ^{2}}{5 ( 4 - x )}

\int_{- 3}^{0} \frac{1}{1 - x} d x

What is the integral of (1-x)^{3/2} ?
The integral of (1-x)^{3/2} is -2/5 (1-x)^{5/2}+C