Indefinite Integration

 $\int_{ }xe^x\ dx$  by using integration by parts.

•  $xe^x-\ e^x+c$  

•  $xe^x+e^x+c$  

•  $xe^x+c$  

•  $xe^x-e^x$  

Evaluate the indefinite integral using integration by parts. 
 $\int t^2\ln t\ dt\$  

•  $\frac{2t^2\ln2t-t^2}{4}+C$  

•  $\frac{t^3\ \ln3}{3}-\frac{t^3}{9}+C$  

•  $\frac{e^t}{2t+2}+C$  

•  $\frac{-2t-1}{4e^{2t}}+C$  

∫(3x⁴+2)⁴(12x³)dx

• ½(3x⁴+2)⁴+C
• (3x⁴+2)⁴+C
• ⅕(3x⁴+2)⁵+C
• ⅓(3x⁴+2)⁶+C

Tags

CCSS.HSA.APR.A.1

∫ 2 x (x²- 3)^(1/2) dx

• (x²- 3)^(3/2)+C

• (3/2)(x²- 3)^(3/2)+C

• (2/3)(x²- 3)^(3/2)+C

• (2/3)(x²- 3)^(-1/2)+C

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

∫ 2 x (x²- 3)^(1/2) dx

• (x²- 3)^(3/2)+C

• (3/2)(x²- 3)^(3/2)+C

• (2/3)(x²- 3)^(3/2)+C

• (2/3)(x²- 3)^(-1/2)+C

∫ 6 x (x² +1 )² dx

• ( x² + 1)³ + C

• 3 ( x² + 1)³ + C

• ( x² + 1)¹ + C

• 6 ( x² + 1)³ + C

Tags

CCSS.HSA.APR.A.1

Find the integral:

• 1/3(x⁴ + 3)³ + c

• 1/12(x⁴ + 3)³ + c

• 3/4(x⁴ + 3)³ + c

• 1/4(x⁴ + 3)³ + c

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Find the integral:

• 1/8(4x² + 3)⁴ + c

• 1/2(4x² + 3)⁴ + c

• 1/32(4x² + 3)⁴ + c

• 1/4(4x² + 3)⁴ + c

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

What is the choice of u for ∫ e^x(1+e^x)^(1/2) dx?

• e^x

• 1+e^x

• (1+e^x)^(1/2)

• (e^x)^(1/2)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Integrate  $\int_{ }^{ }\left(\frac{4\tan\theta}{\sin\theta\cos\theta}\right)d\theta$  

•  $4\tan\theta+C$  

•  $4\sin\theta+C$  

•  $-4\cos\theta+C$  

•  $4\sec\theta+C$