TRY THIS INTEGRAL.

\int \frac{sinx+sin^{3}x}{cos2x}dx = Acosx + Blog\left|f(x) \right| + c

A) A=1/4,B=-\frac{1}{\sqrt{2}}, f(x)=\frac{\sqrt{2}cosx -1}{\sqrt{2}cosx +1}

B) A=1/2,B=-\frac{3}{4\sqrt{2}}, f(x)=\frac{\sqrt{2}cosx +1}{\sqrt{2}cosx -1}

C) none.

ans-----> (B)

1 Answers

Take sinx common from the numerator and write cos2x = 2cos²x - 1..then substitute cosx = t..

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