More on Integration Formulas

​More on Integration Formulas

​Objective

​ Solving Indefinite Integrals involving Logarithmic, Exponential and Trigonometric functions.

 

​Introduction

​Let us first recall the following differentiation formulas of Exponential and Logarithmic functions.

Multiple Choice

Find the derivative of $$f\left(x\right)\ =e^x$$  

• $$e^x$$  

• e

• x

• $$e^x+C$$  

Multiple Choice

Find the derivative of $$f\left(x\right)=a^x$$  

• $$a^x$$  

• $$a^x\ln a$$  

• $$\ln a$$  

• $$a^x\ln a+C$$  

Multiple Choice

Find the derivative of $$f\left(x\right)=\ln x$$  

• $$\frac{1}{x}+C$$  

• $$\ln x$$  

• $$\frac{1}{x}$$  

• $$\ln\left|x\right|+C$$  

​Because antidifferentiation is the inverse operation of differentiation, the following formula should be immediate

​Antidifferentiation Rules Involving Exponential and Logarithmic Functions

Multiple Choice

What is the $$\int\ \frac{9}{x}dx?$$  

• $$9\ln\left|x\right|+C$$   

• 9x + C 

• 9lnx 

• 9ln + C

Multiple Choice

What is the $$\int2e^xdx?$$  

• $$e^x+C$$  

• $$2e^x+C$$  

• $$2e^x$$  

• $$+C$$  

Multiple Choice

What is the $$\int5^xdx?$$  

• $$\ln5+C$$  

• $$5x+C$$  

• $$\frac{5^x}{\ln5}+C$$  

• $$\frac{5^x}{\ln5}-C$$  

Multiple Choice

What is the $$\int2^xdx?$$  

• $$\frac{2^x}{\ln2}+c$$  

• $$2^{x+C}$$  

• $$2^x+c$$  

​Find the antiderivative

​General Rules For The Integral of Exponential and Logarithmic Functions

​Integrate the following

​Integration of Trigonometric Functions

​Recall...

​Integration of Trigonometric Function

​Integrals of Trigonometric Functions