InterviewSolution
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int(sin^3x)/((cos^4 x + 3 cos^2 x+1) tan^(-1) (sec x+ cos x))dx= |
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Answer» `tan^(-1)(sec x+ COS x ) + C` `I=int(SIN^3x)/((cos^4 x + 3 cos^2 x+1) tan^(-1) (sec x+ cos x))dx` `rArr I=int((sin^3x)/(cos^2x))/((cos^2 x + 3+ sec^2 x) tan^(-1) (sec x + cosx ))dx` `rArr I=int1/(1+(sec x + cos x )^2)xx(sin x(1-cos^2x))/(cos^2 x)xx1/(tan^(-1)(sec x + cos x ))dx` `rArr I=int1/(tan^(-1) (sec x + cos x ))xx1/(1+(sec x + cos x )^2) xx (tan x sec x -sinx ) dx` `rArr I=int1/(tan^(-1)(sec x + cos x )) d {tan^(-1) (sec x + cos x)}` `rArr I=log|tan^(-1) (sec x + cos x ) |+C` |
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