What is the integral of 1/((a-x)^3) ?

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

Popular >

integral of 1/((a-x)^3)

integral

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

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

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Substitute back

u = a - x

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

Simplify

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

Add a constant to the solution

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

\frac{sin ( x )}{cos ^{5} ( x )}

cos^{4} (x) sin^{2} (x)

\frac{( e ^{x} - e ^{- x} )}{2}

\frac{x + 1}{x ^{2} + 1}

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

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