Problems on Techniques of Integration

Use the Integration by Parts. Set

$$\left\{\begin{array}{lll} u &=&x\\ dv &=& \cos(x)dx\;. \end{array}\right.$$

Then

$$\left\{\begin{array}{lll} du &=&dx\\ v &=& \sin(x)\;. \end{array}\right.$$

So

$$\int x \cos(x) dx = x \sin(x) - \int sin(x) dx$$

or

$$\int x \cos(x) dx = x \sin(x) - [-\cos(x)] + C = x \sin(x) + \cos(x) + C\;.$$

Detailed Answer.

If you prefer to jump to the next problem, click on Next Problem below.

[Next Problem] [Matrix Algebra] [Trigonometry] [Calculus] [Geometry] [Algebra] [Differential Equations] [Complex Variables]

S.O.S MATHematics home page

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Copyright © 1999-2024 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour