This is a good technique to master, so practice on the following solved problems. Do each problem,
covering the answer first, then check your answer.
PROBLEM 1. Evaluate ∫ sec^2 3 x dx.
Answer: Let u = 3x and du = 3 dx. Then du = dx.
Substitute and integrate.
∫ sec
(^2) u du = tan u + C
Then substitute back.
tan 3x + C
PROBLEM 2. Evaluate dx.
Answer: Let u = 5x − 4 and du = 5 dx. Then du = dx.
Substitute and integrate.
Then substitute back.
(5x − 4) + C
PROBLEM 3. Evaluate ∫ x(4x^2 − 7)^10 dx.
Answer: Let u = 4x^2 − 7 and du = 8x dx. Then du = x dx.
Substitute and integrate.
(^) ∫ u^10 du = u^11 + C
Then substitute back.