Integration by Substitution

Another word for 'integral' is .. .

• Constant
• Derivative
• Antiderivative
• Theorem

What does C represent in an antiderivative?

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

Choose correct 'u' for u-substitution method:
 $\int\left(\frac{2x+1}{x^2+x-2}\right)dx$  

• Let  $u=2x+1$  

• Let  $u=x^2$  

• Let  $u=x^2+x-2$  

• Let  $u=dx$  

 $\int\ 4x^3\left(x^4-1\right)^2\ dx$  

•  $\left(x^4-1\right)^3+c$  

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

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

•  $4\left(x^4-1\right)^3+c$  

Integrate  $\int7x^6\left(x^7+1\right)^8dx$  

•  $\frac{\left(x^7-1\right)^9}{9}+c$  

•  $\frac{\left(x^7+1\right)^9}{9}+c$  

•  $\frac{\left(x^7+1\right)^8}{8}+c$  

•  $\frac{\left(7x^6+1\right)^9}{9}+c$  

• 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

 $\int\frac{\left(\ln x\right)^6}{x}\ dx$  

•  $7\left(\ln x\right)^7+C$  

•  $\frac{\ln^6x}{x^2}+C$  

•  $\frac{1}{7}\left(\ln x\right)^7+C$  

•  $\frac{6}{7}\left(\ln x\right)^7+C$  

 $\int\ \frac{dx}{x\ln x}$  

•  $\ln\left(\ln x\right)+C$  

•  $\left(\ln x\right)^2+C$  

•  $\frac{1}{x^2}+C$  

•  $\frac{\ln x}{x^2}+C$  

 $\int\ \tan^2x\ \sec^2x\ dx$  

•  $\frac{1}{3}\sec^3x+C$  

•  $\frac{1}{3}\tan^3x+C$  

•  $\frac{2}{3}\tan^{\frac{2}{3}}x+C$  

•  $\frac{1}{3}\sec x\ \tan x+C$