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Still confused about integral of ln|sin x|

I don't know why when i'm googling solution for integral of ln|sin x|, the output i clicked always give me the solution integral of log(sin x) but the title is integral of ln|sin x|. Is integral of ln|sin x| equal to integral of log(sin x)?

When i asked the solution to my teacher whom gives that problem, he also confused and make me more confused. He tried many times and always failed.

So, does anyone here know the solution integral of ln|sin x|? Please help me, i am so curious about the answer.

Note by Dina Andini Sri Hardina
3 years, 11 months ago

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If you clicked a link to Wolfram Alpha, then what you saw was, in fact, the integral of what you'd asked for. Wolfram Alpha uses \(\log\) as \(\log_e = \ln\), not \(\log_{10}\). Sotiri Komissopoulos · 3 years, 11 months ago

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The indefinite integral of ln lsin xl cannot be expressed in terms of elementary functions. If you have used Wolfram Alpha, you will see that it uses the special function Li(x), so we can't expect that the integral of ln lsin xl can be expressed in terms of functions we usually encounter like ln x, sin x, cos x, and many others. Rhoy Notes · 2 years, 7 months ago

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multinomial in identical distribution Jayant Sarkar · 3 years, 11 months ago

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If you know Integral Calculus, you may integration by parts. Jayver De Torres · 3 years, 11 months ago

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@Jayver De Torres but how? Dina Andini Sri Hardina · 3 years, 11 months ago

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hey I agree that this integral is very challenging. Firstly, ln|sinx| does not equal log|sinx| nor do their integrals. Secondly, is this a indefinite or definite integral, if so does it have any boundaries? Joel Jablonski · 3 years, 11 months ago

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