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Grade 12Integral Calculus

Integrate
∫(1+cos4x)/(cotx – tanx) dx

Lovey

11 Years agoGrade 12

1 Answer

Jitender Singh

Approved Tutor Answer11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int \frac{1+cos4x}{cotx - tanx}dx$
$I = \int \frac{1+cos4x}{\frac{cosx}{sinx} - \frac{sinx}{cosx}}dx$
$I = \int \frac{(1+cos4x).sinx.cosx}{cos^{2}x-sin^{2}x}dx$
$I = \int \frac{(2cos^{2}2x).sinx.cosx}{cos^{2}x-sin^{2}x}dx$
$I = \int \frac{(cos^{2}2x).sin2x}{cos{2}x}dx$
$I = \int cos2x.sin2xdx$
$I = \frac{1}{2}\int 2cos2x.sin2xdx$
$I = \frac{1}{2}\int sin4xdx$
$I = \frac{-cos4x}{8} + c$

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