Basic Integration

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

•  $\frac{3x^2}{2}$  

•  $\frac{3x^2}{2}+7x+c$  

•  $\frac{x^4}{8}+7x+c$  

•  $\frac{x^4}{8}+c$  

Tags

CCSS.HSA.APR.A.1

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

Integrate  $\sin\left(\frac{x}{2}\right)$  with respect to x

•  $\cos\left(\frac{x}{2}\right)\ +\ c$  

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

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

•  $-\frac{1}{2}\cos\left(\frac{x}{2}\right)\ +\ c$  

Tags

CCSS.HSF.TF.B.7

 $\int6x\left(x+2\right)dx$  

•  $6x^2+12x+C$  

•  $x^{2\ }-2x+C$  

•  $3x^2+6x+C$  

•  $2x^3+6x^2+C$ 

Tags

CCSS.HSA.APR.A.1

Integrate  $\int_{ }^{ }3\ dx$  

• = 0

•  $=\frac{3}{x}+c$  

•  $=\ 3x\ +c$  

•  $=4+c$  

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

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

•  $5x^{\frac{1}{3}}-4e^{-4x}+1+C$  

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

• Got lazy with fake answers

 $\frac{\text{d}x}{\text{d}y}=7x^6-3x^2+5,\ \ y\left(1\right)=1.$  Find y.

•  $y=x^7-x^3+5x+C$  

•  $\frac{7}{6}x^7-\frac{3}{2}x^3+5x-2$  

•  $y=x^7-x^3+5x-4$  

•  $None\ of\ the\ above$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Which curve solves the differential equation and passes through the point (0,2)?

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