Basic Integration

If y = $ax^n$  , then  $\int_{ }^{ }y\ dx\ =$  

•  $\frac{ax^{n+1}}{n+1}$  

•  $\frac{ax^{n-1}}{n-1}+\ c$  
  

•  $\frac{ax^{n+1}}{n}+\ c$  

•  $\frac{ax^{n+1}}{n+1}+\ c$  

Integrate  $\sqrt{x}$  with respect to x

•  $x^{\frac{1}{2}}+c$  

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

•  $\frac{2}{3}x^{\frac{3}{2}}+\ c$  

•  $\frac{3}{2}x^{\frac{3}{2}}+\ c$  

Tags

CCSS.HSN.RN.A.2

 $\int_{ }^{ }\ \frac{1}{x}+\ \frac{1}{x^2}\ dx$  

•  $x^{-1}\ +\ x^{-2}+\ c$  

•  $x^0\ -\ x^{-1}+\ c$  
  

•  $\ln x+\ x^{-1}+\ c$  

•  $\ln x-\ x^{-1}+\ c$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Select the correct syntax and answer for the problem:

• ∫ 2x +1 dx = x² + x

• ∫ 2x +1 dx = x + x² + c

• ∫ 2x +1 = x² + x + c

• ∫ 2x +1 dx =4 x² + x + c

what is the answer for $\int_{ }^{ }\frac{2}{x^2}dx$  ?

•  $\frac{-2}{x}+C$  

•  $-2x^{-1}+C$  

•  $\frac{2}{x}+C$  

•  $2x^{-1}+C$  

 $\int_{ }^{ }\ \ \frac{3}{2x-5}dx=?$  

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

•  $\frac{1}{2}\ln\left|2x-5\right|+C$  

•  $3\ln\left|2x-5\right|+C$  

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

  The statement   $\int_{ }^{ }xdx=\frac{x^2}{2}+C$   ?

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