Integration

Solve  $\int\left(8x^3-2x\right)dx$  

•  $2x^4-x^2+C$  

•  $4x^{4\ }-2x+C$  

•  $x^4-2x+C$  

•  $12x^4-x^2+C$ 

Solve  $\int6x\left(x+2\right)dx$  

•  $6x^2+12x+C$  

•  $x^{2\ }-2x+C$  

•  $3x^2+6x+C$  

•  $2x^3+6x^2+C$ 

Solve  $\int\left(e^{7x}-\frac{5}{2x^3}\right)dx$  

•  $\frac{e^{7x}}{7}-\frac{5}{8x^4}+C$  

•  $\frac{e^{7x}}{7}+\frac{5}{4x^2}+C$  

•  $7e^{7x}-\frac{5}{8x^4}+C$  

•  $\frac{e^{7x}}{8x}+\frac{5}{4x^2}+C$  

• Nothing is correct

Solve $\int_{ }^{ }2\sin\left(\frac{x}{5}\right)dx$  

•  $\cos\left(\frac{x}{5}\right)+C$  

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

•  $-10\cos\left(\frac{x}{5}\right)+C$  

•  $-2\cos\left(5x\right)+C$  

 Solve $\int12x^3\left(3x^4+2\right)^4\ dx$  

•  $\frac{1}{2}\left(3x^4+2\right)^4+C$  
  

•  $5\left(3x^4+2\right)^5+C$  

•  $\frac{1}{5}\left(3x^4+2\right)^5+C$ 

•  $\frac{1}{3}\left(3x^4+2\right)^6+C$  

Solve  $\int_{ }^{ }e^x\cos\left(e^x+6\right)\ dx$  

•  $\frac{1}{6}\cos\left(e^x+6\right)+C$  
  

•  $\sin\left(e^x+6\right)+C$  
  

•  $-\sin\left(e^x+6\right)+C$  
  

•  $\frac{1}{6}e^x\sin\left(e^x+6\right)+C$  
  

What does C represent in an antiderivative?

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

What is an antiderivative?

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