Integration

∫3x²(x³-9)^2/3 dx

• (3x²)^4/3
• (2/3)(x³-9)^5/3
• 3(x³-9)^-1/3
• -3(x³-9)^-1/3

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

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

•  $e^{2x}+\ 6x^2$  

•  $2e^{2x}\ +6x\$  

•  $2e^x+6x\$  

• none of these

 $\int_{ }^{ }e^{5x}dx\ =$  

•  $e^{5x}+c$  

•  $5e^{5x}+c$  

•  $\frac{1}{5}e^{5x}+c$  

• none of these

Tags

CCSS.HSA.SSE.B.3

 $\int\ \frac{2}{x+3}dx^{ }=$  

• 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

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

•  $22\left(2x+1\right)^{11}+c$  

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

•  $11\left(2x+1\right)^{10}+c$  

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

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

•  $\frac{e^{6x}}{6}\ +\ c$  

•  $\frac{e^{9x}}{9}\ +\ c$  

•  $6e^{6x}\ +\ c$  

•  $\left(e^{3x}\right)^2\ +\ c$  

What method would you use here?

• antiderivatives
• u-substitution
• integration by parts
• slope fields

When using u-substitution to integrate this, what is the u?

• 2x

• e^x

• x²

• none of these

This can be integrated using u-substitution. What should "u" equal in this integral?

• x

• (lnx)/x

• lnx

• sin(lnx)

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSF.LE.A.4