# what is the technique to solve this type of integration

$$\int{\sqrt{x-3}(\sin^{-1}(\ln{x})+\cos^{-1}(\ln{x}))\ dx}$$ what is the answer because I have a problem

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Use latex to write the integral properly. Is it $$\int \sqrt{x-3} \cdot {\sin^{-1}(\ln x)+\cos^{-1}(\ln x)}dx$$ ? – Reader Oct 29 '12 at 16:09
@Reader: $\int \sqrt{x-3} \{\sin^{-1}(\ln x)+\cos^{-1}(\ln x)\}\mathrm{d}x$ ? – Prashant Gupta Oct 29 '12 at 16:21

Use the fact that $\arccos a + \arcsin a =\frac {\pi}2$ for $0 \le a \le \frac {\pi}2$
@PrashantGupta You can't integrate $\frac{\pi}2\int\sqrt{x-3}dx$? – Mike Oct 29 '12 at 16:32
@PrashantGupta Try substituting $\sqrt{x-3}=u$. – user43081 Oct 29 '12 at 16:55