Explanation Formula used: “If u and v are differentiable functions, then ∫ u d v = u v − ∫ v d u .” Calculation: The given integral is, ∫ ( 3 x + 6 ) e − 3 x d x . The integrand f ( x ) = ( 3 x + 6 ) e − 3 x is in product of two functions. Solve the above integral by the integration by parts. Let u = 3 x + 6 and d v = e − 3 x d x . Differentiate u = 3 x + 6 as follows. d u d x = 3 d u = 3 d x Integrate d v = e − 3 x d x as follows. ∫ d v = ∫ e − 3 x d x v = − e − 3 x 3 Substitute corresponding values in the formula ∫ u d v = u v − ∫ v d u and simplify

Finite Mathematics and Calculus with Applications

1st Edition

ISBN: 9781323188361

Author: Margaret Lial

Publisher: Pearson Education

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Chapter 16, Problem 21RE

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To find: The functional value of the integral ∫(3x+6)e−3xdx though integration by parts.

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Chapter 16, Problem 20RE

Chapter 16, Problem 22RE

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Chapter 16 Solutions

Finite Mathematics and Calculus with Applications

Ch. 16.1 - Find xe2xdx.Ch. 16.1 - Find ln2xdx.Ch. 16.1 - Prob. 3YT Ch. 16.1 - Find 1ex2lnxdx.Ch. 16.1 - Prob. 5YT Ch. 16.1 - Prob. 1WE Ch. 16.1 - Find the following. W2.(3x52x3)dx Ch. 16.1 - Find the following. W3.(x23+1x)dx Ch. 16.1 - Prob. 4WE Ch. 16.1 - Use integration by parts to find the integrals in...

Ch. 16.1 - Prob. 6WE Ch. 16.1 - Use integration by parts to find the integrals in...Ch. 16.1 - Use integration by parts to find the integrals in...Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Use integration by parts to find the integrals in...Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E Ch. 16.1 - Prob. 11E Ch. 16.1 - Prob. 12E Ch. 16.1 - Prob. 13E Ch. 16.1 - Prob. 14E Ch. 16.1 - Prob. 15E Ch. 16.1 - Prob. 16E Ch. 16.1 - Prob. 17E Ch. 16.1 - Prob. 18E Ch. 16.1 - Prob. 19E Ch. 16.1 - Exercises 1322 are mixedsome require integration...Ch. 16.1 - Prob. 21E Ch. 16.1 - Prob. 22E Ch. 16.1 - Prob. 23E Ch. 16.1 - Prob. 24E Ch. 16.1 - Prob. 25E Ch. 16.1 - Prob. 26E Ch. 16.1 - Prob. 27E Ch. 16.1 - Prob. 28E Ch. 16.1 - What rule of differentiation is related to...Ch. 16.1 - Prob. 30E Ch. 16.1 - Suppose that u and v are differentiable functions...Ch. 16.1 - Prob. 32E Ch. 16.1 - Prob. 33E Ch. 16.1 - Prob. 34E Ch. 16.1 - Prob. 35E Ch. 16.1 - 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Prob. 16E Ch. 16.5 - Prob. 17E Ch. 16.5 - Prob. 18E Ch. 16.5 - Prob. 19E Ch. 16.5 - Find the particular solution for each initial...Ch. 16.5 - Prob. 21E Ch. 16.5 - Prob. 22E Ch. 16.5 - Prob. 23E Ch. 16.5 - Prob. 24E Ch. 16.5 - Prob. 25E Ch. 16.5 - Prob. 26E Ch. 16.5 - Prob. 27E Ch. 16.5 - Prob. 28E Ch. 16.5 - Find the particular solution for each initial...Ch. 16.5 - Prob. 30E Ch. 16.5 - Prob. 31E Ch. 16.5 - Prob. 32E Ch. 16.5 - Prob. 33E Ch. 16.5 - Prob. 34E Ch. 16.5 - Prob. 35E Ch. 16.5 - Prob. 36E Ch. 16.5 - Suppose that 0 y0 N. 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The functional value of the integral ∫ ( 3 x + 6 ) e − 3 x d x though integration by parts.

Solution Summary: The author explains that the functional value of the integral is -(x+2)e-3x, which is in product of two functions.

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To find: The functional value of the integral ∫(3x+6)e−3xdx though integration by parts.

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Chapter 16 Solutions