Solve frac{[cos^-1x{sqrt{(1-x^2)}}]}{log_{e}{1+(frac{sin(2xsqrt{(1-x^2)})}{pi})}}dx

$$\frac { [ \cos ^ { - 1 } x \{ \sqrt { ( 1 - x ^ { 2 } ) } \} ] } { \log _ { e } \{ 1 + ( \frac { \sin ( 2 x \sqrt { ( 1 - x ^ { 2 } ) } ) } { \pi } ) \} } d x$$

Evaluate

$$\frac{dx\sqrt{1-x^{2}}\arccos(x)}{\ln(\sin(2x\sqrt{1-x^{2}})+\pi )-\ln(\pi )}$$

Differentiate w.r.t. x

$$\frac{d\left(-x\sqrt{1-x^{2}}\sin(2x\sqrt{1-x^{2}})\ln(\sin(2x\sqrt{1-x^{2}})+\pi )-2x^{2}\arccos(x)\sin(2x\sqrt{1-x^{2}})\ln(\sin(2x\sqrt{1-x^{2}})+\pi )+4\sqrt{1-x^{2}}x^{3}\arccos(x)\cos(2x\sqrt{1-x^{2}})+\arccos(x)\sin(2x\sqrt{1-x^{2}})\ln(\sin(2x\sqrt{1-x^{2}})+\pi )-2\pi x^{2}\arccos(x)\ln(\sin(2x\sqrt{1-x^{2}})+\pi )-2x\sqrt{1-x^{2}}\arccos(x)\cos(2x\sqrt{1-x^{2}})+2\ln(\pi )x^{2}\arccos(x)\sin(2x\sqrt{1-x^{2}})-\pi x\sqrt{1-x^{2}}\ln(\sin(2x\sqrt{1-x^{2}})+\pi )+\ln(\pi )x\sqrt{1-x^{2}}\sin(2x\sqrt{1-x^{2}})+\pi \arccos(x)\ln(\sin(2x\sqrt{1-x^{2}})+\pi )-\ln(\pi )\arccos(x)\sin(2x\sqrt{1-x^{2}})+2\pi \ln(\pi )x^{2}\arccos(x)-\pi \ln(\pi )\arccos(x)+\pi \ln(\pi )x\sqrt{1-x^{2}}\right)}{\sqrt{1-x^{2}}\left(\sin(2x\sqrt{1-x^{2}})+\pi \right)\left(\ln(\sin(2x\sqrt{1-x^{2}})+\pi )-\ln(\pi )\right)^{2}}$$