Exponential and Logarithmic Integrals

Exponential and Logarithmic Integrals

Multiple Choice

What is an antiderivative?

• The opposite of a derivative
• The same as a derivative
• A second derivative
• It always represents velocity.

Multiple Choice

What does C represent in an antiderivative?

• A variable
• A constant
• None of these
• Unknown

Multiple Choice

 $\int\left(\frac{4}{x}-e_{ }^x\right)dx$  

•  $\frac{4}{x^2}-xe^x+C$  

•  $4\ln\left|x\right|-e^x+C$  

•  $\frac{4}{x^2}-4e^x+C$  

• 
   $4\ln\left|x\right|+e^x+C$  
  

Multiple Choice

 $\int\left(5\sqrt{x^3}-16e^{-4x}+\frac{1}{x}\right)dx$  

•  $2x^{\frac{5}{2}}+4x^{-4x}+\ln\left|x\right|+C$  

•  $5x^{\frac{1}{3}}-4e^{-4x}+1+C$  

•  $\frac{5}{2}x^{\frac{3}{2}}-16e^{-4x}+\ln\left|x\right|+C$  

• Got lazy with fake answers

Multiple Choice

Which of the following is the indefinite integral of  $\frac{x^3}{2}+7$  ?

•  $\frac{3x^2}{2}$  

•  $\frac{3x^2}{2}+7x+c$  

•  $\frac{x^4}{8}+7x+c$  

•  $\frac{x^4}{8}+c$