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What is the Integration by Parts Formula?

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Tags

CCSS.HSA.SSE.A.2

What would you choose for your u here if you used integration by parts?

• x

• sin(x)

• cos(x)

• e^x

What would you choose for your u here if you used integration by parts?

• t

• 3t

• e^2t

• e^t

• don't use IBP, let u = 2t

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.A.2

CCSS.HSF.LE.A.1

What would you choose for your u here if you used integration by parts?

• x

• tan(x)

• arctan(x)

• dx

What would you choose for your u here if you used integration by parts?

• ln(x)

• ln(x)sin(x)

• sin(x)

• x

• A
• B
• C
• D

• A
• B
• C
• D

Solve via integration by parts

• 3t(e^2t)/2 - (e^2t)/4 + C
• 3t(e^2t)⋅2 - 3(e^2t)⋅4 + C
• 3(e^2t) - (e^2t)/4 + C
• 3t(e^2t)/2 - 3(e^2t)/4 + C

Solve via integration by parts

• -x²sin(x) - 2xcos(x) + 2sin(x) + c
• x²sin(x) + 2xcos(x) - 2sin(x) + c
• x²cos(x) + 2xsin(x) - 2cos(x) + c
• -x²cos(x) - 2xsin(x) + 2cos(x) + c

Solve the integral
∫ sin²(x)cos⁵(x)dx

• sin³(x)/3 - 2sin⁵(x)/5 + sin⁷(x)/7
• sin(x) - sin³(x)/3 + c
• cos²(x)/2 - cos⁴(x)/4 + c
• cos³(x)/3 - 2sos⁵(x)/5 + cos⁷(x)/7