Basic Integration 12th

If y = $ax^n$  , then  $\int_{ }^{ }y\ dx\ =$  

•  $\frac{ax^{n+1}}{n+1}$  

•  $\frac{ax^{n-1}}{n-1}+\ c$  
  

•  $\frac{ax^{n+1}}{n}+\ c$  

•  $\frac{ax^{n+1}}{n+1}+\ c$  

Tags

CCSS.HSA.APR.A.1

Integrate  $\int\left(2x+1\right)^{10}\ dx$  with respect to x.

•  $22\left(2x+1\right)^{11}+c$  

•  $\frac{1}{22}\left(2x+1\right)^{11}+c$  

•  $11\left(2x+1\right)^{10}+c$  

•  $\frac{1}{11}\left(2x+1\right)^{10}+c$  

 $\int_{ }^{ }\sec^2\ 5x\ \ dx\ \ =$  

•  $\tan\ x\ \ +\ c$  

•  $\frac{1}{5}\tan\ x\ \ +\ c$  

•  $\frac{1}{5}\tan\ 5x\ \ +\ c$  

•  $\frac{1}{5}\tan^2\ 5x\ \ +\ c$  

Tags

CCSS.HSF.TF.B.7

Integrate  $\sin\left(\frac{x}{2}\right)$  with respect to x

•  $\cos\left(\frac{x}{2}\right)\ +\ c$  

•  $-2\cos\left(\frac{x}{2}\right)\ +\ c$  

•  $-\cos\left(\frac{x}{2}\right)\ +\ c$  

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

Tags

CCSS.HSF.TF.B.7

Find the integral with respect to x of   $\int_{ }^{ }\ \left(e^{3x}\right)^2\ dx\ .$  

•  $\frac{e^{6x}}{6}\ +\ c$  

•  $\frac{e^{9x}}{9}\ +\ c$  

•  $6e^{6x}\ +\ c$  

•  $\left(e^{3x}\right)^2\ +\ c$  

Find indefinite integral for  $\int_{ }^{ }\frac{1}{e^{5x}}\ dx$  

•  $\frac{1}{5}e^{5x}\ +\ c$  

•  $-5e^{4x}\ +\ c$  

•  $\frac{e^{-5x}}{-5}+\ c$  

•  $\frac{e^{-4x}}{-4}+\ c$  

Integrate  $\int_{ }^{ }\left(\frac{1-\sin x}{\cos^2x}\right)dx$  

•  $\tan x-\sec x+c$  

•  $\tan x+\sec x+c$  

•  $\cot x-\operatorname{cosec}x+c$  

•  $\cot x+\operatorname{cosec}x+c$  

Tags

CCSS.HSA.APR.D.6

Integrate $\int_{ }^{ }\left(\frac{\cos2x}{\cos^2x}\right)dx$ 

•  $2x-\tan x+c_{ }$  

•  $2x+\tan x+c$  

•  $x-\tan x+c$  

•  $x+\tan x+c$  

Tags

CCSS.HSA.APR.D.6

Integrate  $\int_{ }^{ }\left(\frac{\cos^2x}{\sin^2x}\right)dx$  

•  $-\cot x-x+c$  

•  $\cot x+x+c$  

•  $-\cot x+x+c$  

•  $\cot x-x+c$  

Tags

CCSS.HSF.TF.B.7

Integrate  $\int_{ }^{ }\left(\cos x-\sin x\right)^2dx$  

•  $x+\frac{1}{2}\cos2x+c$  

•  $x-\frac{1}{2}\cos2x+c$  

•  $x+\cos2x+c$  

•  $x-\cos2x+c$  

Tags

CCSS.HSA.SSE.B.3