Integration: Substitution Method

 $\int\left(x^2+3x+2\right)dx$  

•  $x^3+3x^2+2x+c$  

•  $\frac{x^3}{3}+\frac{3}{2}x^2+2x$  

•  $\frac{x^3}{3}+\frac{3}{2}x^2+2x+c$  

•  $\frac{x^3}{3}+3x^2+2x+c$  

 $\int\left(2\sqrt{x}\right)^{ }dx$  

•  $\frac{2}{3}x^{\frac{3}{2}}+c$  

•  $x^{\frac{3}{2}}+c$  

•  $\frac{4}{3}x^{\frac{3}{2}}+c$  

•  $\frac{x^{\frac{3}{2}}}{2}+c$  

 $\int\left(\frac{3}{x+1}\right)dx$  

•  $3\left(x+1\right)+c$  

•  $\ln\left(3x+1\right)+c$  

•  $\ln\left(x+1\right)+c$  

•  $3\ln\left(x+1\right)+c$  

 $∫e^{2x}dx$  

•  $e^{2x}+c$ 

•  $2e^{2x}+c$  

•  $\frac{1}{2}e^x+c$  

•  $\frac{1}{2}e^{2x}+c$  

 $\int5e^{5x}dx$  

•  $25e^{5x}+c$  

•  $5e^{5x}-1+c$ 

•  $e^{5x}+c$ 

•  $\frac{1}{5}e^{5x}+c$ 

Choose correct method to solve the following integral:
 $\int2x\left(x^2+2\right)^3dx$  

• Substitution Method

• Integration by parts

• Basic rule of integration

• None of the above

Choose correct method to solve the following integral:
 $\int\left(\frac{x^2+2}{3}\right)dx$  

• Substitution method

• Integration by parts

• Basic rule of integration

• None of the above

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  $u=dx$  

Choose correct 'u' to solve the following integral by using substitution method:
 $\int2xe^{x^2}dx$  

• Let  $u=x$  

• Let  $u=x^2$  

• Let  $u=e^{x^2}$  

• Let  $u=2x$  

Solve the following by using substitution method:
 $\int\left(\frac{4x}{2x^2+6}\right)dx$  

•  $\ln\left(2x^2+6\right)+c$  

•  $\ln\left(2x^2+6\right)$  

•  $4x\ln\left(2x^2+6\right)+c$  

•  $4x\ln\left(2x^2+6\right)$