How do you integrate $\int \frac{x^{3}}{x (x^{2} + 2 x + 1)}$ $int x^3/[x(x^2+2x+1)]$ using partial fractions?

Question

How do you integrate $\int \frac{x^{3}}{x (x^{2} + 2 x + 1)}$ $int x^3/[x(x^2+2x+1)]$ using partial fractions?

1 Answer

Impact of this question

1338 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-05T15:47:02

$x - 2 ln | x + 1 | - \frac{1}{x + 1} + C$ $x-2ln|x+1|-1/(x+1)+C$

Explanation:

$\frac{x^{3}}{x (x^{2} + 2 x + 1)} = \frac{x^{2}}{{(x + 1)}^{2}} = {(1 - \frac{1}{x + 1})}^{2}$ $x^3/[x(x^2+2x+1)] = x^2/(x+1)^2 =(1-1/(x+1))^2$
$qquad = 1-2/(x+1)+1/(x+1)^2$

Thus

$int x^3/[x(x^2+2x+1)]dx = int ( 1-2/(x+1)+1/(x+1)^2)dx$
$qquad = x-2ln|x+1|-1/(x+1)+C$

Science

Math

Humanities

... and beyond

How do you integrate $\int \frac{x^{3}}{x (x^{2} + 2 x + 1)}$ $int x^3/[x(x^2+2x+1)]$ using partial fractions?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you integrate int x^3/[x(x^2+2x+1)]∫x3x(x2+2x+1)int x^3/[x(x^2+2x+1)] using partial fractions?

1 Answer

Explanation:

Related questions

Impact of this question

How do you integrate $\int \frac{x^{3}}{x (x^{2} + 2 x + 1)}$ $int x^3/[x(x^2+2x+1)]$ using partial fractions?