Indefinite Integrals of Logarithmic Functions 1

Quiz summary

0 of 5 questions completed

Questions:

–

You have already completed the quiz before. Hence you can not start it again.

Quiz is loading...

You must sign in or sign up to start the quiz.

You have to finish following quiz, to start this quiz:

Lets see your results!

Points

Score

Time

Retry Quiz

Question 1 of 5

1. Question
Find the integral

$$\int{\frac{5}{x}} dx$$
- `5 ln x+c`
- `ln x+c`
- `5 ln 5x+c`
- ` ln 5x+c`
Hint

Help Video

Correct

Great Work!

Incorrect

Integral of a Fraction

$$\int{\frac{1}{\color{#004ec4}{x}}}dx=\log_e \color{#004ec4}{x}+c$$

Substitute the components into the formula

$$\int{\frac{1}{\color{#004ec4}{x}}}dx$$ `=` $$\log_e \color{#004ec4}{x}+c$$

$$\int{\frac{5}{\color{#004ec4}{x}}}dx$$ `=` $$5\int{\frac{1}{\color{#004ec4}{x}}}dx$$ Take out the constant `5`

`=` $$5\ln \color{#004ec4}{x}+c$$ Substitute known values

`5 ln x+c`

Question 2 of 5

Find the integral

$$\int3x^2+4x-{\frac{6}{x}} dx$$

`x^3+2x^2-6 ln x+c`
`x^3-2x^2-6 ln x+c`
`6 ln x+c`
`x^3-2x^2+6 ln x+c`

Question 3 of 5

Find the integral

$$\int{\frac{dx}{x+5}} dx$$

`ln (x+5)+c`
`5 lnx+c`
`(x+5) ln (x+5)+c`
`5ln (x+5)+c`

Question 4 of 5

Find the integral

$$\int{\frac{2x}{x^2+1}} dx$$

`ln (x^2+1)+c`
`x^2+1+c`
`(x^2+1)ln (x^2+1)+c`
`xln (x+1)+c`

Question 5 of 5

Find the integral

$$\int{\frac{1}{4x-7}} dx$$

`1/4 ln (4x-7)+c`
`4 ln (4x-7)+c`
`ln (4x-7)+c`
`-7 ln (4x-7)+c`

	$$\int 3x^2+4x-{\frac{6}{\color{#004ec4}{x}}}dx$$

`=`	$$\frac{3x^3}{3}+\frac{4x^2}{2}-6\int{\frac{1}{\color{#004ec4}{x}}}dx$$	Take out the constants and integrate

`=`	$$x^3+2x^2-6\ln x+c$$	Simplify

$$\int \frac{\color{#9a00c7}{f'(x)}}{\color{#D800AD}{f(x)}}$$	`=`	$$\int \frac{\color{#9a00c7}{1}}{\color{#D800AD}{x+5}}$$

	`=`	`1/1`	Differentiate the denominator

	`=`	`1`

`f(x)`	`=`	`x+5`
`f'(x)`	`=`	`1`

$$\int \frac{\color{#9a00c7}{f'(x)}}{\color{#D800AD}{f(x)}}dx$$	`=`	$$\log_e [\color{#D800AD}{f(x)}]+c$$

$$\int \frac{\color{#9a00c7}{dx}}{\color{#D800AD}{x+5}}dx$$	`=`	$$\ln [\color{#D800AD}{x+5}]+c$$	Substitute known values

$$\int \frac{\color{#9a00c7}{f'(x)}}{\color{#D800AD}{f(x)}}$$	`=`	$$\int \frac{\color{#9a00c7}{2x}}{\color{#D800AD}{x^2+1}}$$

	`=`	`(2x)/(2x)`	Differentiate the denominator

	`=`	`1`

Indefinite Integrals of Logarithmic Functions 1

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Great Work!

Integral of a Fraction

2. Question

Hint

Correct!

Integral of a Fraction

3. Question

Hint

Keep Going!

Indefinite Integral

4. Question

Hint

Fantastic!

Indefinite Integral

5. Question

Hint

Excellent!

Indefinite Integral

Quizzes

$$\int{\frac{5}{\color{#004ec4}{x}}}dx$$	`=`	$$5\int{\frac{1}{\color{#004ec4}{x}}}dx$$	Take out the constant `5`

	`=`	$$5\ln \color{#004ec4}{x}+c$$	Substitute known values

$$\int \frac{\color{#9a00c7}{f'(x)}}{\color{#D800AD}{f(x)}}$$	`=`	$$\int \frac{\color{#9a00c7}{1}}{\color{#D800AD}{4x-7}}$$

	`=`	`1/4`	Differentiate the denominator

$$\frac{1}{4}\int \frac{\color{#9a00c7}{f'(x)}}{\color{#D800AD}{f(x)}}dx$$	`=`	$$\frac{1}{4}\log_e [\color{#D800AD}{f(x)}]+c$$

$$\frac{1}{4}\int \frac{\color{#9a00c7}{4}}{\color{#D800AD}{4x-7}}dx$$	`=`	$$\frac{1}{4}\int \frac{\color{#9a00c7}{4}}{\color{#D800AD}{4x-7}}$$

	`=`	$$\frac{1}{4} \ln [\color{#D800AD}{4x-7}]+c$$	Substitute known values