Indefinite Integration

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.HSA.APR.D.6

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

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

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

•  $-2\cot x-x-2\operatorname{cosec}x+c$  

•  $2\cot x-x+2\operatorname{cosec}x+c$  

•  $-2\cot x-x+2\operatorname{cosec}x+c$  

•  $2\cot x-x-2\operatorname{cosec}x+c$  

Integrate  $\int_{ }^{ }\left(\cot x-\tan x\right)^2dx$  

•  $-\cot x-4x+\tan x+c$  

•  $-\cot x-4x-\tan x+c$  

•  $\cot x-4x-\tan x+c$  

•  $\cot x-4x+\tan x+c$  

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

•  $-\frac{3}{2}x+\frac{1}{4}\sin2x+\tan x+c$  

•  $-\frac{3}{2}x+\frac{1}{2}\sin2x+\tan x+c$  

•  $-\frac{3}{2}x-\frac{1}{4}\sin2x+\tan x+c$  

•  $-\frac{3}{2}x-\frac{1}{2}\sin2x+\tan x+c$  

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

•  $-\cot x-\operatorname{cosec}x+c$  

•  $-\cot x+\operatorname{cosec}x+c$  

•  $\cot x+\operatorname{cosec}x+c$  

•  $\cot x-\operatorname{cosec}x+c$  

Integrate  $\int_{ }^{ }\left(\frac{\cos2x}{1-\cos^22x}\right)dx$  

•  $-\frac{1}{2}\operatorname{cosec}2x+c$  

•  $\frac{1}{2}\operatorname{cosec}2x+c$  

•  $-\frac{1}{2}\sec2x+c$  

•  $\frac{1}{2}\sec2x+c$  

Evaluate the indefinite integral using integration by parts. 
 $\int3x\ e^{2x}\ dx\$  

•  $-\frac{xe^{2x}}{2}+\frac{e^{2x}}{4}+C$  

•  $\frac{3xe^{2x}}{2}-\frac{3e^{2x}}{4}+C$  

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

•  $-\frac{xe^{2x}}{2}+\frac{\ln e^{2x}}{4}+C$