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

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

Popular >

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

integral

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

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

Solution steps

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

Complete the square

x^{2} + 2 x + 1 : (x + 1)^{2}

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

Apply u-substitution

: \int \frac{1}{u ^{4}} d u

= \int \frac{1}{u ^{4}} d u

Apply the Power Rule

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

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

Substitute back

u = x + 1

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

Add a constant to the solution

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

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

\frac{( 6 x + 3 )}{( x ^{2} + 1 )}

\frac{( 1 + a )}{( 1 - a )}

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

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

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