U-Substitution Quiz Review

Integrate the following indefinite integral via u-substitution $\int_{ }^{ }2x\left(x^2+4\right)^3dx$  

•  $\frac{\left(x^2+4\right)^4}{2}+C$  

•  $\frac{\left(x^2+4\right)^4}{4}+C$  

•  $2x\left(x^2+4\right)^4+C$  

•  $6x\left(x^2+4\right)^2+C$  

Integrate the following indefinite integral via u-substitution $\int_{ }^{ }\left(2+2x\right)e^{\left(4x+2x^2\right)}dx$  

•  $\frac{1}{2}e^{\left(4x+2x^2\right)}+C$  

•  $2e^{\left(4x+2x^2\right)}+C$  

•  $e^{\left(2\left(4x+2x^2\right)\right)}+C$  

•  $e^{\left(\frac{1}{2}\left(4x+2x^2\right)\right)}+C$  

Integrate the following indefinite integral via u-substitution $\int_{ }^{ }\left(3x^2+1\right)\sec\left(3x^3+3x\right)\tan\left(3x^3+3x\right)dx$  

•  $3\sec\left(3x^3+3x\right)+C$  

•  $3\tan\left(3x^3+3x\right)+C$  

•  $\frac{1}{3}\tan\left(3x^3+3x\right)+C$  

•  $\frac{1}{3}\sec\left(3x^3+3x\right)+C$  

Integrate the following indefinite integral via u-substitution $\int_{ }^{ }-5\csc^2\left(x\right)\cot\left(x\right)dx$  

•  $\frac{5\cot\left(x\right)}{2}+C$  

•  $\frac{\cot\left(x\right)}{2}+C$  

•  $\frac{\cot^2\left(x\right)}{2}+C$  

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

Evaluate the following definite integral via u-substitution  $\int_0^118x^2\left(2x^3+1\right)^2dx$  

• $26$

• $1$

• $\frac{26}{3}$

• $\frac{1}{3}$

Evaluate the following definite integral via u-substitution  $\int_0^1\frac{6x}{\left(3x^2+1\right)^2}dx$  

• $\frac{3}{4}$

• $-\frac{5}{4}$

• $\frac{21}{64}$

• $\frac{65}{192}$