Сalculate the integral. \int_{0}^{3}\frac{dx}{x^{2}+3}

permaneceerc

permaneceerc

Answered question

2021-10-18

Сalculate the integral.
03dxx2+3

Answer & Explanation

SchepperJ

SchepperJ

Skilled2021-10-19Added 96 answers

Step 1
Given integral:
03dxx2+3
Step 2
Now,
Apply Integral Substitution: x=3u
dx=3du
And:
At x=0u=0
At x=3u=3
That is:
031x2+3dx=0313(u2+1)du
Take the constant out: af(x)dx=af(x)dx
=13031u2+1du
Use the common integral: 1u2+1du=arctan(u)
=13[arctan(u)]3
=13[π30]
=π33

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?