106x+1 = t
\int \frac{1}{t^{5}.\sqrt{t^{2}-1}}dt
t = secθ
\int \frac{sec \theta tan \theta}{sec^{5} \theta tan \theta}d \theta
\int cos^{4}\theta d \theta
\hspace{-16}\mathbf{(1)\;\;\int_{0}^{1}\frac{1-2e^x\sin x}{(e^x+\cos x).(e^x+\sin x)}dx}$\\\\\\ $\mathbf{(2)\;\;\int\frac{1}{(x+1)^5.\sqrt{x^2+2x}}dx}
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3 Answers
106
1708after editing::
\hspace{-16}(1)\;\;\int_{0}^{1}\frac{(1-2e^x.\sin x)}{(e^x+\cos x).(e^x-\sin x)}dx\\\\\\