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November 01, 2025, 03:20:25 pm
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Author Topic: Integral of (tanx)^3  (Read 1132 times)  Share 

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sarahg51

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Integral of (tanx)^3
« on: August 02, 2012, 07:49:26 am »
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Hey everyone
Can someone please help me,

How do I integrate (tanx)^3

Thanks in advance :)
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studynotes

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Re: Integral of (tanx)^3
« Reply #1 on: August 02, 2012, 11:56:12 am »
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dont know if this is right but i let (tan(x))^3= sin(x)^3/cos(x)^3
and then went on from there as i already found the intergral of sinx^3 and cosx^3.
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thushan

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Re: Integral of (tanx)^3
« Reply #2 on: August 02, 2012, 12:11:44 pm »
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Quote from: studynotes on August 02, 2012, 11:56:12 am
dont know if this is right but i let (tan(x))^3= sin(x)^3/cos(x)^3
and then went on from there as i already found the intergral of sinx^3 and cosx^3.

tan^3 (x) = tan(x) (sec^2 (x) - 1) = tan(x) sec^2 (x) - tan(x)

Antiderivative = 1/2 tan^2 (x) + log |cos(x)| + c.
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sarahg51

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Re: Integral of (tanx)^3
« Reply #3 on: August 02, 2012, 04:12:19 pm »
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thanks so much! that makes sense :)
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