Integration by Parts

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?

• 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

Evaluate the indefinite integral using integration by parts. u and  dv are provided.
 $\int x^{4\ }\ln x\ dx\ ;\ \ u=\ln x,\ dv\ =x^4$  

•  $\frac{e^x}{4x+4}+C$  

•  $\frac{2x^{\frac{3}{2}}\ln4x}{3}-\frac{4x^{\frac{3}{2}}}{9}+C$  

•  $\frac{\left(4x^2-1\right)\cdot e^{4x^2}}{32}+C$  

•  $\frac{x^5\ln x}{5}-\frac{x^5}{25}+C$  

 $\int_{ }\left(2x+5\right)^3dx$  

•  $\frac{\left(2x+5\right)^4}{8}$  

•  $\frac{\left(2x+5\right)^4}{8}+c$  

•  $\frac{\left(2x-5\right)^4}{8}+c$  

•  $\frac{\left(2x+5\right)^3}{8}+c$  

 $\int_{ }\frac{2x+1}{x^2+x+1}dx$  

•  $\ln\left|u\right|$  

•  $\ln\left|u\right|+c$  

•  $\ln\left|x^2+x+1\right|+c$  

•  $\ln\left|x^2+x+1\right|$