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integration of 1/ (sin^3 x + …

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integration of 1/ (sin^3 x + cos^3 X)

Posted by Akshat Gupta 7 years, 2 months ago

CBSE > Class 12 > Mathematics

4 answers

Prashant Chaudhary 7 years, 2 months ago

You suppose inte.is integration sign. Then inte dx/(sinx + cosx) (sin^2x-sinxcosx+cos^2x) inte dx/(sinx+cosx) (1-sinxcosx) devide and multiply by 2 2 inte dx/(sinx+cosx) (2-2sinxcosx) 2 inte dx/(sinx+cosx) (2-sin2x) Multiply and devide by sinx+cosx 2 inte (sinx+cosx)dx/(sinx+cosx)^2 (2-sin2x) Let (sinx+cosx)^2=1+sin2x 2 inte (sinx+cosx)dx/(1+sin2x) (2-sin2x) Put cosx-sinx=t Squaring on both side (Cosx-sinx)^2=t^2 1-sin2x=t^2 Sin2x=1-t^2 cosx-sinx=t -(sinx+cosx)dx=dt 2 inte dt/(2-t^2)(2-1+t^2) -2 inte dt/(2-t^2)(1+t^2) Now use partial fraction.

Prashant Chaudhary 7 years, 2 months ago

Use identity (a^3+b^3)=(a+b) (a^2-ab+b^2)

Amandeep Kumar 7 years, 2 months ago

Then take tan x = t

Amandeep Kumar 7 years, 2 months ago

Divide numerator and denominator by cos cube x

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