Advertisement Remove all ads

Evaluate the following. ∫1x2+4x+29 dx - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Sum

Evaluate the following.

`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx

Advertisement Remove all ads

Solution

Let I = `int 1/(sqrt("x"^2 + 4"x"+ 29))` dx

`= int 1/sqrt("x"^2 + 2 * 2"x" + 4 - 4 + 29)` dx

`= int 1/(sqrt(("x + 2")^2 + 25)` dx

`= int "dx"/(sqrt(("x + 2")^2 + 5^2)`

`= log |("x + 2") + sqrt(("x + 2")^2 + 5^2)|`+ c

∴ I = `= log |("x + 2") + sqrt("x"^2 + "4x" + 29)|` + c

Notes

[Note: Answer in the textbook is incorrect.]

Concept: Methods of Integration: Integration by Substitution
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×