integration by substitution radicals

 $\int15x^4\sqrt{3x^5-2}dx$  

•  $\frac{2}{3}\sqrt{\left(3x^5-2\right)^3}+C$  

•  $3x^5\sqrt{\frac{1}{2}x^6-2x}+C$  

•  $\frac{3}{2}\sqrt{\left(3x^5-2\right)^3}+C$  

•  $\sqrt{\left(3x^5-2\right)^3}+C$  

 $\int80x^3\sqrt{5x^4+3}dx$  

•  $\frac{8}{3}\sqrt{\left(5x^4+3\right)^3}+C$  

•  $6\sqrt{\left(5x^4+3\right)^3}+C$  

•  $\sqrt{\left(5x^4+3\right)^3}+C$  

•  $20x^4\sqrt{x^5+3x}+C$  

 $\int\left(2\sqrt{x}\right)^{ }dx$  

•  $\frac{2}{3}x^{\frac{3}{2}}+c$  

•  $x^{\frac{3}{2}}+c$  

•  $\frac{4}{3}x^{\frac{3}{2}}+c$  

•  $\frac{x^{\frac{3}{2}}}{2}+c$  

• A

• B

• C

• D

Choose correct 'u' for u-substitution method:
 $\int\left(\frac{2x+1}{x^2+x-2}\right)dx$  

• Let  $u=2x+1$  

• Let  $u=x^2$  

• Let  $u=x^2+x-2$  

• Let  $u=dx$  

 $∫e^{2x}dx$  

•  $e^{2x}+c$ 

•  $2e^{2x}+c$  

•  $\frac{1}{2}e^x+c$  

•  $\frac{1}{2}e^{2x}+c$  

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

What should be used for u in the integral?

• no u needed
• 4t²
• t³
• 1/4t²

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

what is the choice of u for the integration?

• 4x

• 2x²+6

• 1/(2x²+6)

• ln(2x²+6)