Integration Basics

 $\frac{d}{dx}\left[e^{2x}\ +\ 3x^2+5\right]$  

•  $e^{2x}+\ 6x^2$  

•  $2e^{2x}\ +6x\$  

•  $2e^x+6x\$  

• none of these

 $\frac{d}{dx}\left[\ln\ u\right]$  

•  $\frac{u'}{u}$  

•  $\frac{du}{u}$  

•  $\frac{1}{u}du$  

• all of these

 $\frac{d}{dx}\left[\ln2x\right]$  

•  $\frac{2}{x}+c$  

•  $\frac{2}{x}$  

•  $\frac{2}{2x}=\frac{1}{x}$  

• none of these

If y = ln(3x + 1), then y' =

• $\frac{3x+1}{3}$

• $\frac{3}{3x+1}$

• $\frac{3}{3x+1}+c$

• none of these

if y = e^3x+2, then y' =

• 3e^3x+2

• ⅓e^3x+2

• e^3x+2

• none of these

Rewrite using properties of logs:  $\ln\ \sqrt{3x\ +\ 2}$  

•  $\ln\sqrt{3x}\ +\ \ln\sqrt{2}$  

•  $\frac{1}{2}\ln\left(3x+2\right)$  

• 3(lnx) + ln2

• none of these

 $\frac{d}{dx}\left[\ln\sqrt{3x}\right]=$  

•  $\frac{1}{2\left(3x\right)}$  

•  $\frac{1}{\sqrt{3x}}$  

•  $\frac{3}{2\left(x\right)}$  

•  $\frac{1}{2x}$  

 $\int_{ }^{ }e^{5x}dx\ =$  

•  $e^{5x}+c$  

•  $5e^{5x}+c$  

•  $\frac{1}{5}e^{5x}+c$  

• none of these

Tags

CCSS.HSA.SSE.B.3

∫(cos x + 3x²)dx =

• -sin x + x³ + c

• sinx + x³ + c

• -sin x + 6x

• 🌞

Tags

CCSS.HSA.APR.A.1

 $\int\ \frac{2}{x+3}dx^{ }=$  

• 2ln|x+3| + c

• 2ln(x + 3) + c

•  $\frac{1}{2}\ln\left|x\ +\ 3\right|\ +\ c$  

• none of these

Tags

CCSS.HSF.BF.B.5