Write a value of ∫ elog sinx cosx dx.

1.	Write a value of ∫ elog sinx cosx dx.
Answer» Given, ∫ e^{log sinx} cosx dx = ∫sin x cos x dx (∵e^logx = x) Let sin x = t Differentiating on both sides we get, Cos x dx = dt Substituting above equations in given equation we get, = ∫t dt = \(\frac{t^2}{2}\) + c = \(\frac{sin^2x}{2}\) + c

Answer»

Given,

∫ e^{log sinx} cosx dx

= ∫sin x cos x dx

(∵e^logx = x)

Let sin x = t

Differentiating on both sides we get,

Cos x dx = dt

Substituting above equations in given equation we get,

= ∫t dt

= \(\frac{t^2}{2}\) + c

= \(\frac{sin^2x}{2}\) + c

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