Trigonometric substitutions Evaluate the following integrals using trigonometric

FobelloE

FobelloE

Answered question

2021-10-07

Trigonometric substitutions Evaluate the following integrals using trigonometric substitution.
dxx3x21,x>1

Answer & Explanation

Alannej

Alannej

Skilled2021-10-08Added 104 answers

Consider the provided integral,
dxx3x21,x>1
Evaluate the following integrals using trigonometric substitution.
Apply the trigonometric substitution let x=sec(u)dx=sec(u)tan(u)du
So,
dxx3(x21)=sec(u)tan(u)dusec3(u)sec2(u)1
=tan(u)sec2(u)tan(u)du
=1sec2(u)du
Using trigonometric identity simplifying further,
dxx3x21=cos2(u)du
=1+cos(u)2du
=12(1du+cos(2u)du)
=12(u+12sin(2u))+C
Substitute back x=sec(u).
dxx3x21=12(arcsec(x)+12arcsec(x))+C
Hence.

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