If I=∫cos2xsinx+sin3xdx=Pcosx+Qlog∣f(x)∣+R, then (a)P=21,Q=−423 (b) P=41,Q=21 (c)f(x)=2cosx−12cosx+1 (d) f(x)=2cosx+12cosx−1

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Question

If $I = \int \frac{sin x + sin ^{3} x}{cos 2 x} d x = P cos x + Q lo g ∣ f (x) ∣ + R,$ then (a) $P = \frac{1}{2}, Q = - \frac{3}{4 2}$ (b) $P = \frac{1}{4}, Q = \frac{1}{2}$ (c) $f (x) = \frac{2 cos x + 1}{2 cos x - 1}$ (d) $f (x) = \frac{2 cos x - 1}{2 cos x + 1}$

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I = \int \frac{sin x + sin ^{3} x}{cos 2 x} d x = P cos x + Q lo g ∣ f (x) ∣ + R,

then (a)

P = \frac{1}{2}, Q = - \frac{3}{4 2}

(b)

P = \frac{1}{4}, Q = \frac{1}{2}

(c)

f (x) = \frac{2 cos x + 1}{2 cos x - 1}

(d)

f (x) = \frac{2 cos x - 1}{2 cos x + 1}

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Question Text

I = \int \frac{sin x + sin ^{3} x}{cos 2 x} d x = P cos x + Q lo g ∣ f (x) ∣ + R,

then (a)

P = \frac{1}{2}, Q = - \frac{3}{4 2}

(b)

P = \frac{1}{4}, Q = \frac{1}{2}

(c)

f (x) = \frac{2 cos x + 1}{2 cos x - 1}

(d)

f (x) = \frac{2 cos x - 1}{2 cos x + 1}