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Material Type: Assignment; Class: Calculus II; Subject: Mathematics; University: University of Illinois - Urbana-Champaign; Term: Fall 2008;
Typology: Assignments
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Problem 1. 6.1 #24:
4 x + 4
5 + 2x + x^2
dx
Solution. Using the u-substitution u = 5 + 2x + x
2 , du = (2 + 2x) dx, we have
∫ 4 x + 4
5 + 2x + x^2
dx =
2 du
u
= 2 ln |u| + C
= 2 ln |5 + 2x + x
2 | + C.
Problem 2. 6.1 #32:
x + x
dx
Solution. Using the u-substitution u =
x, du =
1 2
√ x
dx, we have
x + x
dx =
2 du
1 + u
= 2 ln |1 + u| + C
= 2 ln |1 +
x| + C
