
Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Hints and techniques for solving various integration problems. It covers methods such as substitution, partial fraction decomposition, integration by parts, and the use of identities. The document also includes examples of harder integration problems and their respective solutions. This resource is ideal for students and researchers in mathematics and related fields who need assistance in solving complex integrals.
Typology: Assignments
1 / 1
This page cannot be seen from the preview
Don't miss anything!
If you just want to check your answers, use Maple (be aware Maple may present the answer in a superficially different form than you obtain; try simplifying Maple’s answer MINUS your answer to see if you get zero).
∫ cos^2 (u) du. Now use the identity cos^2 (u) = 1/2 + cos(2u)/4.
Harder Problem Hints
x +
1 + x), dv = dx. Do the remain- ing integral with the substitution u =
x + 1.
y, then integrate by parts with u = arcsin(z). Finish the remaining integral with the substitution z = sin(t) and use the identity sin^2 (t) = 1/ 2 − cos(2t)/2.
x + 1, followed by the substitution q =
√ 1 +
u (you could amalgamate the substitutions, but it’s alge- braically less error-prone to do it in two steps.) By the way, Maple won’t touch this integral!