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

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

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

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

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

Solution steps

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

Apply the Power Rule

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

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

Substitute back

u = x - 3

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

Add a constant to the solution

= - \frac{2}{( x - 3 ) ^{\frac{1}{2}}} + C

x \to 0 lim (\frac{2 x + 1}{x ^{3}})

e^{e^{x} + x}

\frac{4}{2 x + 3}

\int \frac{x ^{3}}{5 x ^{2} + 3} d x

\int \frac{1}{( x ^{2} + 25 ) ^{3}} d x

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