Why does Mathematica 10.3.1 fail me on : Integrate[(x^3) [Log[2 Sin[x]]]^8, {x, 0, Pi}] [closed]

All it gives me is a pretty restatement of my original request. When I use WolframAlpha PRO, I get a result of 624510 and a visual representation of the area in question. I know the ends of the interval [0,pi] are problematic. What am I doing wrong? The 'definite integral' in WolframAlpha PRO was given x^3*ln(2*sin(x))^8 in the 'function to integrate' box. Ideally, what would be best, is if both programs would give me a closed form expression, if it exists. NIntegrate was not helpful either. You should know I am very new to Mathematica.

closed as off-topic by Daniel Lichtblau, RunnyKine, m_goldberg, march, user9660 Mar 30 '16 at 4:17

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Daniel Lichtblau, RunnyKine, m_goldberg, march, Community
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• Partly because square brackets are reserved in Mathematica for containing arguments to functions. Parentheses () are the only symbols used in Mathematica for grouping terms and factors in mathematical expressions. That said, I ran that integral in my copy of Mathematica and it returned unevaluated, suggesting that it doesn't know an analytic form (which doesn't mean it doesn't exist; perhaps the expression could be massaged into a form that can be integrated analytically). – march Mar 29 '16 at 18:53

NIntegrate[x^3*Log[2*Sin[x]]^8, {x, 0, π}]

Plot[x^3*Log[2*Sin[x]]^8, {x, 0, π}, Filling -> Axis]