Completing the square Evaluate the following integrals. \int \frac{dx}{x^{2}+6x+18}

a2linetagadaW 2021-10-27 Answered
Completing the square Evaluate the following integrals.
dxx2+6x+18
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Szeteib
Answered 2021-10-28 Author has 102 answers
Step 1
The given integral is dxx2+6x+18.
Evaluate the above integral as follows.
Step 2
dxx2+6x+18=dx(x+3)232+18
=dx(x+3)29+18
=dx(x+3)2+9
=dx(x+3)2+32
=13tan1(x+33)+C
Thus, dxx2+6x+18=13tan1(x+33)+C.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-05-23
Find the indefinite integral ln(x3)dx (a) using a table of integrals and (b) using the Integration by parts method.
asked 2022-08-05
Determine convergence / divergence of sin π n 2 .
Let a n = sin π n 2 .
I attempted the integral test but on the interval [ 1 , 2 ) it is increasing and decreasing on ( 2 , ). So the integral test in only applicable for the decreasing part. + the integral computation seems to lead to 3 pages of steps...
I believe the comparison test would be the most reasonable test, graphically I observed that a n behaves like b n = 1 / n when n is large.
b n = ; but, since b n > a n inconclusive for divergence/convergence.
I attempted the limit comparison, and ratio test, but inconclusive. I am uncertain if I am doing them properly.
How could I bound below a n to proceed with the comparison test? Is there a more appropriate method? How would you proceed?
asked 2021-10-10
Evaluate the integrals
14(1+u)12udu
asked 2021-01-15
To make: A true statement by inserting a symbol <, > or = between the given numbers 0.6and56.
asked 2021-11-16
Evaluate the integral.
024x2dx
asked 2021-09-25

Evaluate the definite integral.
011+7x3dx

asked 2020-10-28
True or False: In many applications of definite integrals, the integral is used to compute the total amount of a varying quantity.

New questions