Integration-By Substitution Method

 $\int\cot x.\log\sin xdx=$  

•  $\left(\log\cot x\right)^2+c$  

•  $\left(\log\sin x\right)^2$  

•  $\left(\log\cos x\right)^2$  

• None of these

 $\int x.\cos x^2dx=$  

•  $x^2.\sin x^3\ +c$  

•  $\frac{\sin x^2}{2}+c$  

•  $\frac{\cos x^2}{2}+c$  

• none of these

Integrate this followings by using Substitution Method
 $\int8x\left(4x^2+5\right)^9dx$  

•  $\frac{\left(4x^2+5\right)^{10}}{10}\ +c$  

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

•  $\frac{\left(8x+5\right)^{10}}{10}\ +c$  

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

Integrate  $\int\frac{2x}{\sqrt{3+x^2}}dx$  using substitution methods

•  $\frac{1}{2\left(3+x^2\right)^{\frac{1}{2}}}+c$  

•  $\left(3+2x\right)^{\frac{1}{2}}+c$  

•  $2\left(3+x^2\right)^{\frac{1}{2}}+c$  

•  $2\left(3+x^2\right)^{-\frac{1}{2}}+c$  

Integrate  $\int7x^6\left(x^7+1\right)^8dx$  

•  $\frac{\left(x^7-1\right)^9}{9}+c$  

•  $\frac{\left(x^7+1\right)^9}{9}+c$  

•  $\frac{\left(x^7+1\right)^8}{8}+c$  

•  $\frac{\left(7x^6+1\right)^9}{9}+c$  

 $\int_{ }\frac{2x+1}{x^2+x+1}dx$  by using method of substitution.

•  $\ln\left|u\right|$  

•  $\ln\left|u\right|+c$  

•  $\ln\left|x^2+x+1\right|+c$  

•  $\ln\left|x^2+x+1\right|$  

Tags

CCSS.HSA.APR.D.6

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  $u=2x$  

∫(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

 $\int15x^4\sqrt{3x^5-2}dx$  

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

•  $3x^5\sqrt{\frac{1}{2}x^6-2x}+C$  

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

•  $\sqrt{\left(3x^5-2\right)^3}+C$  

 $\int_{ }\left(3\tan x+4\right)^5\sec^2x\ dx$  by using method of substitution.

•  $\left(3\tan x\ +4\right)^6+c$  

•  $\frac{\left(3\tan x\ +4\right)^6}{6}$  

•  $\frac{\left(3\tan x\ -4\right)^6}{6}+c$  

•  $\frac{\left(3\tan x\ +4\right)^6}{6}+c$