Techniques of Integration

 $\int u\ du\$  is a method of

• By Parts

• Substituition

• Partial Fraction

• Integration

Integrate this followings by using Substitution Method
 $\int8x\left(4x^2+5\right)^9dx$  

•  $\frac{\left(4x^2+5\right)^{10}}{10}\ +c$  

•  $\frac{\left(4x^2+5\right)^8}{8}\ +c$  

•  $\frac{\left(8x+5\right)^{10}}{10}\ +c$  

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

Integrate $\int x\left(x^2+5\right)^7dx$  by using substituition method

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

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

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

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

Change this $\int6x\left(3x^2-4\right)^5dx$  in term of  $u$  

•  $\int u^4du$  

•  $\int u^5du$  

•  $\int u^6du$  

•  $\int u^7du$  

 $\int5x^4\left(x^5-7\right)^3dx$  can solves with

• integration by parts

• substituition method

• partial fraction

• multiplication method

What would you choose for your u here if you used integration by parts?

• x
• x⁴
• e^-x
• e^x

Solve via integration by parts

• 3t(e^2t)/2 -(e^2t)/4 + C

• 3t(e^2t)⋅2 - 3(e^2t)⋅4 + C

• 3(e^2t) - (e^2t)/4 + C

• 3t(e^2t)/2 - 3(e^2t)/4 + C

What would you choose for your u here if you used integration by parts?

• ln x

• ln (x) sin (x)

• sin (x)

• x

Which technique should be used to integrate this?

• product rule

• u-substitution

• by parts

• algebra re-write

Which technique should be used to integrate this:

• antiderivatives

• u-substitution

• integration by parts

• partial fraction