Integration by Inspection

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

Which of the following is the indefinite integral of  $\frac{3}{x^4}\ \ ?$ 

•  $-\frac{1}{x^3}+\ c$  

•  $\frac{3}{5x^5}+\ c$  
  

•  $-\frac{12}{x^5}+\ c$  

•  $\frac{1}{x^3}+\ c$  

Integrate  $\int\left(2x+1\right)^{10}\ dx$  with respect to x.

•  $22\left(2x+1\right)^{11}+c$  

•  $\frac{1}{22}\left(2x+1\right)^{11}+c$  

•  $11\left(2x+1\right)^{10}+c$  

•  $\frac{1}{11}\left(2x+1\right)^{10}+c$  

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

•  $x^{-1}\ +\ x^{-2}+\ c$  

•  $x^0\ -\ x^{-1}+\ c$  
  

•  $\ln x+\ x^{-1}+\ c$  

•  $\ln x-\ x^{-1}+\ c$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

 $\int_{ }^{ }\sec^2\ 5x\ \ dx\ \ =$  

•  $\tan\ x\ \ +\ c$  

•  $\frac{1}{5}\tan\ x\ \ +\ c$  

•  $\frac{1}{5}\tan\ 5x\ \ +\ c$  

•  $\frac{1}{5}\tan^2\ 5x\ \ +\ c$  

Tags

CCSS.HSF.TF.B.7

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

Find the integral with respect to x of   $\int_{ }^{ }\ \left(e^{3x}\right)^2\ dx\ .$  

•  $\frac{e^{6x}}{6}\ +\ c$  

•  $\frac{e^{9x}}{9}\ +\ c$  

•  $6e^{6x}\ +\ c$  

•  $\left(e^{3x}\right)^2\ +\ c$  

• ln(2x²+6) + C
• ln(2x²+6)(4x) + C
• 1/(2x²+6) + C
• 1/(2x²+6)² + C

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

∫ 2x cos(x²) dx

• sin(x²) + C

• 2 sin ( 2x ) + C

• (1/2) sin(x²) + C

• 4 cos(2x ) + C

∫ 2 x (x²- 3)^(1/2) dx

• (x²- 3)^(3/2)+C
• (3/2)(x²- 3)^(3/2)+C
• (2/3)(x²- 3)^(3/2)+C
• (2/3)(x²- 3)^(-1/2)+C

Tags

CCSS.HSA.APR.A.1

CCSS.HSN.RN.A.2