What is the integral of 1/((4-x)^{3/2)} ?

The integral of 1/((4-x)^{3/2)} is 2/((4-x)^{1/2)}+C

Popular >

integral of 1/((4-x)^{3/2)}

\int \frac{1}{( 4 - x ) ^{\frac{3}{2}}} d x

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

Solution steps

\int \frac{1}{( 4 - x ) ^{\frac{3}{2}}} d x

Apply u-substitution

: \int - \frac{1}{u ^{\frac{3}{2}}} d u

= \int - \frac{1}{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 \frac{1}{u ^{\frac{3}{2}}} d u

Apply the Power Rule

: - \frac{2}{u ^{\frac{1}{2}}}

= - (- \frac{2}{u ^{\frac{1}{2}}})

Substitute back

u = 4 - x

= - (- \frac{2}{( 4 - x ) ^{\frac{1}{2}}})

Simplify

= \frac{2}{( 4 - x ) ^{\frac{1}{2}}}

Add a constant to the solution

= \frac{2}{( 4 - x ) ^{\frac{1}{2}}} + C

n = 1 \sum \infty \frac{5 n}{4 n + 7}

\frac{8}{( s ^{2} + 1 ) ( s ^{2} - 1 )}

\int \frac{a ^{2} - x ^{2}}{x ^{4}} d x

x \to 2 lim (x + 3)

What is the integral of 1/((4-x)^{3/2)} ?
The integral of 1/((4-x)^{3/2)} is 2/((4-x)^{1/2)}+C