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The following integral can be evaluated by using substitution: a) b) Identify the inside function. u= x^4+1 Differentiate: 4x^3 47³ Make dr the subject: dz Rewrite the whole integral in terms of u and du: f Simplify and cancel I's: Integrate with respect to u: 3/2 149 3 N/W * du +1 ✔ 149 x √= 3x^3 sqrt(u) 3x³ √2¹ +1 dz du 4x^3

The following integral can be evaluated by using substitution: a) b) Identify the inside function. u= x^4+1 Differentiate: 4x^3 47³ Make dr the subject: dz Rewrite the whole integral in terms of u and du: f Simplify and cancel I's: Integrate with respect to u: 3/2 149 3 N/W * du +1 ✔ 149 x √= 3x^3 sqrt(u) 3x³ √2¹ +1 dz du 4x^3

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.2: Substitution
Problem 31E: Use substitution to find each indefinite integral. e2xe2x+5dx
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answer part A last part ,tow part in part b and part c . thanks 

c) Hence write down the indefinite integral: (Don't forget the constant of integration as this is an indefinite integral.) 32³ 1¹ +1 dz
Transcribed Image Text:c) Hence write down the indefinite integral: (Don't forget the constant of integration as this is an indefinite integral.) 32³ 1¹ +1 dz
The following integral can be evaluated by using substitution: a) b) Identify the inside function. u= x^4+1 I¹ + Differentiate: 4x^3 Make de the subject: dx = Rewrite the whole integral in terms of u and du: f Simplify and cancel z's: 3/2 Integrate with respect to u: 149 * du 149 * 3x³ √2¹ +1 1= 3x^3 sqrt(u) dz du 4x^3
Transcribed Image Text:The following integral can be evaluated by using substitution: a) b) Identify the inside function. u= x^4+1 I¹ + Differentiate: 4x^3 Make de the subject: dx = Rewrite the whole integral in terms of u and du: f Simplify and cancel z's: 3/2 Integrate with respect to u: 149 * du 149 * 3x³ √2¹ +1 1= 3x^3 sqrt(u) dz du 4x^3
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can you help me with the parts i got wrong . thanks 

c) Hence write down the indefinite integral: -5 ln (42) dr (Don't forget the constant of integration as this is an indefinite integral.) 5x-5x 1n(4x)+c 5x -5x ln(4x) + c *
Transcribed Image Text:c) Hence write down the indefinite integral: -5 ln (42) dr (Don't forget the constant of integration as this is an indefinite integral.) 5x-5x 1n(4x)+c 5x -5x ln(4x) + c *
The following integral may be evaluated by using integration by parts. Notes: • powers can be entered using ^ to divide, use / a) du The product-5 In(4x) must be written in the form u Determine u,and u: b) Apply the integration by parts formula: U= V= fudr = fudr = In(4x) -5X -5 ln(42) dz uv >> 뿜 1/X -5 Rie - S X -S -5 >> > dz dr
Transcribed Image Text:The following integral may be evaluated by using integration by parts. Notes: • powers can be entered using ^ to divide, use / a) du The product-5 In(4x) must be written in the form u Determine u,and u: b) Apply the integration by parts formula: U= V= fudr = fudr = In(4x) -5X -5 ln(42) dz uv >> 뿜 1/X -5 Rie - S X -S -5 >> > dz dr
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