Find integral \int\frac{\sqrt{x^{2}-9}}{x}dx

Reeves

Reeves

Answered question

2021-10-15

Find integral x29xdx

Answer & Explanation

Margot Mill

Margot Mill

Skilled2021-10-16Added 106 answers

Step 1
Consider the integrals.
x29xdx
Let,
x=3sec(t)
Differentiating with respect to "t"
dx=3sec(t)tan(t)dt
Step 2
Substituting all value in given integrals,
x29xdx=9sec2t93sec(t)3sec(t)tan(t)dt
=3sec2t13sec(t)3sec(t)tan(t)dt
=3tan(t)tan(t)dt
=3tan2(t)dt
Further solving it,
=3(sec2(t)1)dt    sec2(t)1=tan2(t)
=3(tantt)+C
=3[tan(sec1(x3))sec1(x3)]+C
=3sec1(x3)+x29+C

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