Find the value of the constant C for which the integral \int^\infty_0\lef

Ramsey

Ramsey

Answered question

2021-10-23

Find the value of the constant C for which the integral
0(xx2+1C3x+1)dx
converges. Evaluate the integral for this value of C.

Answer & Explanation

Usamah Prosser

Usamah Prosser

Skilled2021-10-24Added 86 answers

Step 1
0(xx2+1C3x+1) dx =limt0t(xx2+1C3x+1) dx 
Integrate the integral on the right first.
0t(xx2+1C3x+1) dx =(12ln|x2+1|C3ln|3x+1|)0t
=16(ln(x2+1)3ln(3x+1)2C)0t
=16ln(x2+1)3(3x+1)2C0t
=16ln(t2+1)3(3t+1)2C16ln11
=16ln(t2+1)3(3t+1)2C
Therefore
0(xx2+1C3x+1) dx =limt(16ln(t2+1)(3t+1)2C)
=16ln(limt(t2+1)3(3t+1)2C)
 

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