Integration lesson 18.01.2021

The process of finding an antiderivative is called ...

(a)  

I cannot use the inverse (a)   to find all anti-derivatives.

I can use “drop-shadow” backwards to integrate:

• Trigonometric functions

• Logarithmic Functions

• Polynomials

• Exponential Functions

 $\int_{ }^{ }\sin x\ dx$  =                    (use a space between function and variable, as well as between variable and C

(a)  

What is

 $\int_{ }^{ }\cos\ 2x\ dx\ =\ ...?$  

•  $\sin2x+C$  

•  $-2\ \sin\ 2x\ +C$  - 2 sin 2x + C
  

•  $-\frac{1}{2}\cos\ 2x\ +\ C$  

•  $-2\ \cos\ 2x\ +C$  

 $\int_{ }^{ }e^{7x}dx\ =\ \ \ \ \ ...?$  

•  $7e^{7x}$  

• $$7e^{7x}$$ + C
  

•  $\frac{e^{7x}}{7}+C$  

 $\int\ \frac{3}{3x+2}dx\ =\ .....?$  

•  $3\left(3x+2\right)^{-2}+C$  

•  $\ln\left(3x+2\right)+C$  

 $\int\frac{1}{\cos^2x}dx\ =\ ....\ ?\$  

•  $\tan\ x\ +\ C$  

•  $\cos^{-3}x\ +\ C$  

•  $-\frac{\cos^{-3x}\ }{3}+C$