Integration by parts Key words LO Class work

Integration by parts Key words: LO: Class work: Homework: 16 January 2022

Integration by parts If we want to integrate the product of two functions, where one of the functions is not related to the derivative of the other, such as x cos x. An expression such as this can only be integrated using the method of integration by parts. Since the derivative of the product of two functions u and v is obtained using the product rule: where u and v are functions of x. So then, Integrating with respect to x gives: www. mathssupport. org

Integration by parts Rearranging: To integrate a product using this formula we let one part equal u and the other equal We find . by differentiating the part we called u. We find v by integrating the part we called It is important to choose u and so that is easier to integrate than www. mathssupport. org . .

Integration by parts So, to integrate x cos x with respect to x: Let and differentiate integrate So Now, using the formula Substituting Integrating Simplifying www. mathssupport. org We don’t need the “+ c” here.

Integration by parts Find and Let So Now, apply the formula Substituting Integrating Simplifying www. mathssupport. org :

Integration by parts Find We don’t know the integral of ln x so: and let so Now, using the formula, Substituting Simplifying Integrating Simplifying www. mathssupport. org

Integration by parts Find We don’t know the integral of ln x so: let and so Now, using the formula, Substituting Simplifying Integrating Simplifying www. mathssupport. org