Exam 3 Review

 $\int_{ }^{ }5x^{-4}dx$  

•  $c-\frac{5}{3x^3}$  

•  $\frac{5}{3x^3}+c$  

•  $-\frac{5}{3}x^3+c$  

•  $-x^{-5}+c$  

 $\int_{ }^{ }\left(x+1\right)\left(2x-3\right)dx$  

•  $\frac{2}{3}x^3-\frac{x^2}{2}-3x+c$  

•  $\frac{2}{3}x^2-\frac{x}{2}-3+c$  

•  $\left(\frac{x^2}{2}+x\right)\left(x^2-3x\right)+c$  

•  $\frac{2}{3}x^3-\frac{x^2}{2}+3x+c$  

 $\int_{ }^{ }8\left(1+2x\right)^{-3}dx=\frac{-2}{\left(1+2x\right)^2}+c$  

• CORRECT/ BETUL

• WRONG/ SALAH

∫ t⁶ dt

• 6t⁵
• 6t⁵ + C
• 1/7 t⁷ + C
• t⁷ + C

∫ 4 dx

• 0
• 4t + C
• 4x + C
• 2x² + C

Evaluate the indefinite integral.

 $\int_{ }^{ }\left(2x+2x^{-3}-6x^{-4}\right)dx$  

•  $x-x^{-3}+2x^4+C$  

•  $-2x+C$  

•  $x^2-x^{-2}+2x^{-3}+C$  

•  $2x^2+2x^{-2}-6x^{-3}+C$  

 $\int e^xdx\ is\ equal\ to$  

•  $\frac{e^x}{x}+c$  

•  $e^x+c$  

•  $e^x$  

•  $\frac{e^x}{\ln\left(e\right)}$  

Identify the u and the du.

• u = 3x², du = -6x dx

• u = x³ + 1, du = 3x² dx

• $u=\sqrt{x^{3^{ }}+1}$ , $du=\frac{3x^2}{2\sqrt{x^3+1}}$

• $u=\sqrt{x^3+1}$ , $du\ =\ 3x^2dx$

Find the antiderivative : $\int_{ }^{ }\ \frac{4}{7x}dx$   

•  $-\frac{4}{7}\ \ln\left(x\right)\ +c$  

•  $\frac{4}{7}\ln\left(x\right)+c$  

•  $\frac{4}{7}x\ +c$  

•  $\frac{4}{7}\ln\left(x\right)$  

What is an Antiderivative?

• The opposite of a derivative

• The same as a derivative

• A second derivative

• It always represents velocity