What is the integral of 1/((x+a)^2) ?

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

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integral of 1/((x+a)^2)

integral

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

- \frac{1}{x + a} + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = x + a

= - \frac{1}{x + a}

Add a constant to the solution

= - \frac{1}{x + a} + C

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

\frac{2 x}{x + 2}

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

(sin (x) + cos^{2} (x))^{3}

\frac{2 ^{x}}{ln ( 2 )}