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1. Find the antiderivatives of the following functions using the substitution rule. Write your answers on a separate sheet of paper. a. (5x+4) dx b./√x-5dx c. f sin¹(x) cos(x) dx d. fdx

1. Find the antiderivatives of the following functions using the substitution rule. Write your answers on a separate sheet of paper. a. (5x+4) dx b./√x-5dx c. f sin¹(x) cos(x) dx d. fdx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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APPLICATION 1. Find the antiderivatives of the following functions using the substitution rule. Write your answers on a separate sheet of paper. a. [(5x + 4)5dx b. √ √4x-5dx c. sin¹0 (x) cos(x) dx d. fdx II. Find and correct the mistakes in the following "solutions to these integration problems. Write the new solutions in the space provided below. a. [sin 5x dx;u= 5x, du = 5dx sin 5x dx = = [₁ sin u du = -cos u + C = -5 cos 5x + C 9 cost_dx;Mm. sản x, du = cosx dx 1+ an cos x du -dx = 1+ SIR²X 1+u² c. f(4x + 1)(2x² + x) dx;u= 2x² + x, du = 4x + 1 [(4x + 1 x + b. = In||1 + u²| + C = In|1+ sin³x|+C 1)(2x² + x) dx = [uħdu = ²(2x²+x) + C
Transcribed Image Text:APPLICATION 1. Find the antiderivatives of the following functions using the substitution rule. Write your answers on a separate sheet of paper. a. [(5x + 4)5dx b. √ √4x-5dx c. sin¹0 (x) cos(x) dx d. fdx II. Find and correct the mistakes in the following "solutions to these integration problems. Write the new solutions in the space provided below. a. [sin 5x dx;u= 5x, du = 5dx sin 5x dx = = [₁ sin u du = -cos u + C = -5 cos 5x + C 9 cost_dx;Mm. sản x, du = cosx dx 1+ an cos x du -dx = 1+ SIR²X 1+u² c. f(4x + 1)(2x² + x) dx;u= 2x² + x, du = 4x + 1 [(4x + 1 x + b. = In||1 + u²| + C = In|1+ sin³x|+C 1)(2x² + x) dx = [uħdu = ²(2x²+x) + C
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