Use substitution to find the indefinite integral. \int \frac{-4x}{x^{2}+3}dx

Stefan Hendricks

Stefan Hendricks

Answered question

2021-12-16

Use substitution to find the indefinite integral.
4xx2+3dx

Answer & Explanation

Jacob Homer

Jacob Homer

Beginner2021-12-17Added 41 answers

Step 1
Integration is summation of discrete data. The integral is calculated for the functions to find their area, displacement, volume, that occurs due to combination of small data.
Integration is of two types definite integral and indefinite integral. Indefinite integral are defined where upper and lower limits are not given, whereas in definite integral both upper and lower limit are there.
Step 2
Solve the indefinite integral 4xx2+3dx using substitution method. Substitute x2+3 as t in the given integral.
t=x2+3
dtdx=d(x2+3)dx
dtdx=2x
dx=dt2x
Substitute value of dx=dt2x in integration 4xx2+3dx we get 4xt(dt2x)=2tdt
Step 3
Solve the integral 2tdt for t we get
2tdt=2ln|t|+C...(1)
Substitute value of t=x2+3 in equation (1)
2ln|t|+C=2ln|x2+3|+C
Therefore, integration of 4xx2+3dx is 2ln|x2+3|+C
trisanualb6

trisanualb6

Beginner2021-12-18Added 32 answers

It is required to calculate:
4xx2+3dx
Substitution u=x2+3dudx=2xdx=12xdu:
=21udu
Now we calculate:
1udu
This is the well-known tabular integral:
=ln(u)
We substitute the already calculated integrals:
21udu
=2ln(u)
Reverse replacement u=x2+3:
=2ln(x2+3)
Problem solved:
4xx2+3dx
=2ln(x2+3)+C
nick1337

nick1337

Expert2021-12-28Added 777 answers

4xx2+3dx
Transform the expression
2tdt
Use properties of integrals
2×1tdt
Evaluate the integral
2ln(|t|)
Substitute back
2ln(|x2+3|)
Calculate the absolute value
2ln(x2+3)
Add C
Solution
2ln(x2+3)+C

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?