Quiz #1

What should be split off, so that it is the "du" part?

 $\int\sin_{ }^4x\cos^5x\ dx$  

• du = tan x

• du = sin x

• du =  cos x

• du = - sin x

What can this integral look like after making a u-substitution?

 $\int_{ }^{ }\tan^{-\frac{11}{2}}x\ \sec^6x\ dx$  

•  $\int_{ }^{ }u^5\left(1-u^2\right)^2du$  

•  $\int u^{-\frac{11}{2}}\left(1+u^2\right)^2du$  

•  $\int u^{-\frac{11}{2}}\left(1-u^2\right)^2du$  

•  $\text{}\int u^{-\frac{11}{2}}\left(1+u^2\right)du$  

Solve/integrate the following:

 $\int-12e^{-2x}\cot\left(6e^{-2x}+9\right)dx$  

•  $\ln\left|\cos\left(6e^{-2x}+9\right)\right|+C$  

•  $\ln\left|\sin\left(6e^{-2x}+9\right)\right|+C$  

•  $\ln\left|\tan\left(6e^{-2x}+9\right)\right|+C$  

• No idea...