Integration - Trigonometric Expressions & Reverse Chain Rule

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

•  $\sin^3x\ +c$  

•  $\frac{1}{3}\sin^3x\ +c$  

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

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

 $\int_{ }^{ }\sin^2x\cos x\ dx$  

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

•  $\sin^3x+c$  

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

•  $\frac{1}{3}\sin^3x+c$  

 $\int_{ }^{ }\cos^2x\ \sin x\ dx$  

•  $\cos^3x+c$  

•  $\frac{1}{3}\cos^3x+c$  

•  $\frac{1}{3}\sin^3x+c$  

•  $-\frac{1}{3}\cos^3x+c$  

 $\int_{ }\sec^2x\ dx$  

•  $\tan x+c$  

•  $\sec^3x+c$  

•  $\frac{1}{3}\sec^3x+c$  

•  $-\tan x+c$  

 $\int_{ }^{ }\tan^2x\ dx$  

•  $\tan^3x+c$  

•  $\frac{1}{3}\tan^3x+c$  

•  $\tan x-x+c$  

•  $-\cot x-x+c$  

 $\int_{ }^{ }3x^2\left(x^3+4\right)^2\ dx$  

•  $\left(x^3+4\right)^3+c$  

•  $\frac{1}{3}\left(x^3+4\right)^3+c$  

•  $\frac{1}{6}\left(x^3+4\right)^3+c$  

•  $x^3\left(x^3+4\right)^3+c$  

 $\int\left(\frac{2x+5}{x^2+5x}\right)dx$  

•  $\frac{x^2+5x}{\frac{1}{3}x^3+\frac{5}{2}x^2}+c$  

•  $\ln\left(x^2+5x\right)+c$  

•  $\ln\left|x^2+5x\right|+c$  

Which of the squared trig expressions can be integrated using an identity?

•  $\sin^2x\ \&\ \cos^2x$  

•  $\tan^2x\ \&\ \cos^2x$  

•  $\operatorname{cosec}^2x\ \&\ \tan^2x$  

•  $\tan^2x\ \&\cot^2x$  

For which of the squared trigonometric expressions should you apply a double angle formulae?

• $\sin^2x\ \&\ \cot^2x$

• $\tan^2x\ \&\ \cot^2x$

• $\sin^2x\ \&\ \cos^2x$

Tags

CCSS.HSF.TF.C.9

 $\int_{ }^{ }\sec^2x\ \tan^2x\ dx$  

•  $\sec^3x+c$  

•  $\frac{1}{3}\sec^3x+c$  

•  $\tan^3x+c$  

•  $\frac{1}{3}\tan^3x+c$