Integrate using an appropriate formula from the table of integrals. State the formula number, u and du, identify any constants, and show any constant “adjustments” "Multiply by 1” if needed. 2 lntt√1+5lntdt 16.17.18.19.20.21.22.[²√a + bu du =TuS1u√a+bu[³S-S1√√a+bua + buนa + buUn-du-du =U√a + budu =-duun/a + bu=du =du=2b (2n + 3)1√á-In2-[uº{(a + bu)²"'* _ na fu²+¹ √/a + bu du]³/2--1a (n − 1)√a+bu - √a√a+bu + √a:arctana (n − 1)(2n +2√a+bu+aaf.-2 (2a - bu)36²√a + buun-1a + bu2+ 1)6 (2²-a+1u√a + bu| (2n − 3)b ſ25 ( u² √a + bu -+ C, a > 0−117 [(a + dujt², (2n = 536 / Va + bu du] ·bu) ³/2- 5)b √a+2UT-1a + bu + C+C, a <0du1un-1√a+bunaªf.un-1√a + bududu9n #1n #1

Answered: 2 lnt tyl + 5 lnt dt

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Calculus

2 lnt tyl + 5 lnt dt

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter5: Factoring Polynomials

Section5.8: Factoring Pattern For X2+bx+c, C Negative

Problem 10MRE

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Question

Integrate using an appropriate formula from the table of integrals. State the formula number, u and du, identify any constants, and show any constant “adjustments” "Multiply by 1” if needed.

16.
17.
18.
19.
20.
21.
22.
[²√a + bu du =
Tu
S
1
u√a+bu
[³
S-
S
1
√√a+bu
a + bu
น
a + bu
Un
-du
-du =
U
√a + bu
du =
-du
un
/a + bu
=
du =
du
=
2
b (2n + 3)
1
√á
-In
2
-[uº{(a + bu)²"'* _ na fu²+¹ √/a + bu du]
³/2
-
-1
a (n − 1)
√a+bu - √a
√a+bu + √a
:arctan
a (n − 1)
(2n +
2√a+bu+a
af.
-2 (2a - bu)
36²
√a + bu
un-1
a + bu
2
+ 1)6 (2²
-a
+
1
u√a + bu
| (2n − 3)b ſ
2
5 ( u² √a + bu -
+ C, a > 0
−1
17 [(a + dujt², (2n = 536 / Va + bu du] ·
bu) ³/2
- 5)b √a
+
2
UT-1
a + bu + C
+C, a <0
du
1
un-1√a+bu
na
ªf.
un-1
√a + bu
du
du
9
n #1
n #1

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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