How do you integrate $\int x^{2} sin x d x$ $int x^2 sin x dx$ using integration by parts?

Question

How do you integrate $\int x^{2} sin x d x$ $int x^2 sin x dx$ using integration by parts?

1 Answer

Impact of this question

3789 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-07T02:15:39

$I = - x^{2} cos (x) + 2 x sin (x) + 2 cos (x) + c$ $I = -x^2cos(x) + 2xsin(x) + 2cos(x) + c$

Explanation:

Say $u = x^{2}$ $u = x^2$ so $d u = 2 x$ $du = 2x$ , $d v = sin (x)$ $dv = sin(x)$ so $v = - cos (x)$ $v = -cos(x)$

$I = - x^{2} cos (x) + 2 \int x cos (x) d x$ $I = -x^2cos(x) +2intxcos(x)dx$

Say $u = x$ $u = x$ so $d u = 1$ $du = 1$ , $d v = cos (x)$ $dv = cos(x)$ so $v = sin (x)$ $v = sin(x)$

$I = - x^{2} cos (x) + 2 x sin (x) - 2 \int sin (x) d x$ $I = -x^2cos(x) + 2xsin(x) - 2intsin(x)dx$
$I = - x^{2} cos (x) + 2 x sin (x) + 2 cos (x) + c$ $I = -x^2cos(x) + 2xsin(x) + 2cos(x) + c$

Science

Math

Humanities

... and beyond

How do you integrate $\int x^{2} sin x d x$ $int x^2 sin x dx$ using integration by parts?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you integrate int x^2 sin x dx ∫x2sinxdxint x^2 sin x dx using integration by parts?

1 Answer

Explanation:

Related questions

Impact of this question

How do you integrate $\int x^{2} sin x d x$ $int x^2 sin x dx$ using integration by parts?