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.HSA.APR.D.7

CCSS.HSF.BF.B.5

 $\int5x^4dx$  

•  $x^5$  

•  $\frac{5}{4}x^5+C$  

•  $x^5+C$  

•  $20x^3$  + C

Tags

CCSS.HSA.APR.A.1

∫ 2x cos(x²) dx

• sin(x²) + C

• 2 sin ( 2x ) + C

• (1/2) sin(x²) + C

• 4 cos(2x ) + C

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

Tags

CCSS.HSA.APR.D.7

CCSS.HSF.BF.B.5

Use the indicated substitution to evaluate the integral.

 $\int\sin\left(2x\right)\ dx,\ \ \ \ \ \ u=2x$  

•  $\cos\left(2x\right)+C$  

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

•  $-\cos\left(2x\right)+C$  

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

Use substitution to evaluate the integral $\int4\sec^24x\ \sqrt{\tan4x}\ dx$

• $2\left(\tan4x\right)^{\frac{3}{2}}+C$

• $\frac{15}{4}\cdot\left(\tan4x\right)^{\frac{4}{3}}+C$

• $\frac{4}{3}\cdot\left(\tan4x\right)^{\frac{3}{2}}+C$

• $\frac{2}{3}\cdot\left(\tan4x\right)^{\frac{3}{2}}+C$

Use the indicated substitution to evaluate the integral.

 $\int x\left(x^2+5\right)^7dx\ ,\ \ \ \ u\ =\ x^2+5$  

•  $\frac{\left(2x+5\right)^8}{8}+c$  

•  $\frac{\left(x^2+5\right)^8}{16}+c$  

•  $\frac{\left(x^2+5\right)^6}{6}+c$  

•  $\frac{\left(2x+5\right)^8}{16}+c$  

Tags

CCSS.HSA.SSE.B.3

Use the indicated substitution to evaluate the integral.

 $\int\frac{2x}{\sqrt{3+x^2}}dx\ ,\ \ \ u=3+x^2$  

•  $\frac{1}{2\sqrt{3+x^2}}+C$  

•  $\sqrt{3+x^2}+C$  

•  $2\sqrt{3+x^2}+C$  

•  $\frac{2}{\sqrt{3+x^3}}+C$