Exam 2 solutions

8.1 Basic Integration Rules

	(8x − 17)15

dx

u = 8x − 17, du = 8 dx, n = 15.

Use

	un

du.

	20 x (19 − 2 x )

dx

u = 19 − 2

x

, du = −

1

x

dx

Use

	du u

.

Solution or Explanation

	7 (7t − 8)2 + 4 dt

u = 7t − 8, du = 7 dt, a = 2

Use

	du u2 + a2 .

Solution or Explanation

	2 81 − t2

dt

u = t, du = dt, a = 9

Use

	du a2 − u2

.

Solution or Explanation

	5 (5t − 10)2 + 16 dt

u = 5t − 10, du = 5 dt, a = 4

Use

	du u2 + a2 .

Solution or Explanation

	5 16 − t2

dt

u = t, du = dt, a = 4

Use

	du a2 − u2

.

	t

sec(3t²) dt

u = 3t², du = 6t dt

Use

	sec(u)

du

Solution or Explanation

	(10cos(14x))esin(14x) dx

u = sin(14x), du = 14cos(14x) dx

Use

	eu

du.

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