another Integral

\hspace{-16}(1)::\mathbf{\int e^{\sin x}\left(\frac{x.\cos^3 x-\sin x}{\cos^2 x}\right)dx}\\\\\\ (2)::\mathbf{\int\frac{\sin x.\cos x}{\sin x+\cos x}dx}$

3 Answers

1
narayan ·

2)\int \frac{sinx.cosx}{(sinx+cosx)} dx =\frac{1}{2}\int \frac{(sinx+cosx)^2-1}{sinx+cosx} dx

\frac{1}{2} \left ( \int \left ( sinx+cosx \right )dx -\int \frac{dx}{sinx+cosx} \right ){ }

\frac{1}{2}\left ( \int sinx\, dx + \int cosx\, dx + \int \frac{dx}{sinx+cosx}\right )

\frac{1}{2}\left ( -cosx+ sinx-\frac{1}{\sqrt{2}}\ln \left | \tan\left ( \frac{x}{2} + \frac{1}{2}\tan^{-1}(1) |\right )
\frac{1}{2}\left ( -cosx+ sinx-\frac{1}{\sqrt{2}}\ln \left | \tan\left ( \frac{x}{2} + \frac{\pi }{8} \right )\right |\right )+c

341
Hari Shankar ·

2) esin x(x - sec x)

1708
man111 singh ·

Thanks bhatt sir, Got it.

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