Explanation Given information: ∫ x ( 1 + x ) 3 d x Concept and Formula Used: ∫ 1 d x = x + C & ∫ cos x d x = sin x + C , ∫ x n d x = n x n − 1 + C . Integral by Substitution Calculation: It is given that ∫ x ( 1 + x ) 3 d x Let 1 + x = t Differentiate with respect to‘ t ’ both sides d d t ( 1 + x ) = d d t t d x d t = 1 d x = d t Substitute the value of d x & 1 + x = t in the integral The integrand becomes ∫ ( t − 1 ) ( t ) 3 d t

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 7.1, Problem 27PS

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To Derive: ∫x(1+x)3dx

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Chapter 7.1, Problem 26PS

Chapter 7.1, Problem 28PS

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2. Find the following definite and indefinite integrals. O Parts a, b, and c: For the indefinite integrals, you do not need to simplify your final O a. answer. Parts d and e: For the definite integrals, simplify your answer and write your answer in exact form. Do not use a calculator. [(x-3 + 5x5/2+√3)dx [(-e² +13) dx d. e. (²2-√x) dx (ex - x)dx L² (2x - J-3 (2x - 1)dx O

Solve for x. 4x 7 F 9. A. 6 OB. 15.75 O C. 3 OD. D. 9

(x*+1)dx For items 9 and 10, refer to f 9. What is the degree of the polynomial in the numerator and denominator? What type of rational fraction is given and how will you solve the integral?

Chapter 7 Solutions

Calculus

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To Derive: ∫ x ( 1 + x ) 3 d x

Solution Summary: The author explains how to subtract the value of dx&1+x=t in the integral.

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Chapter 7 Solutions