How vày you find the integral of displaystylefleft(x ight)=frac11-sinx using integration by parts?
https://socratic.org/questions/how-do-you-find-the-integral-of-f-x-1-1-sinx-using-integration-by-parts
displaystyle anx+secx+C Explanation: displaystyleintfracleft.dx ight.1-sinx Let's first get this into a more workable size by multiplying through ...

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How vị you differentiate displaystylefleft(x ight)=fracx1-sinx using the quotient rule?
displaystylef'left(x ight)=frac1-sinx+xcosxleft(1-sinx ight)^2 Explanation:letdisplaystylef=xanddisplaystyleg=1-sinx ...
Hint: dfrac1xleft(1-dfracsin xx ight)=dfracx-sin xx^3cdot x Now use Are all limits solvable without L'Hôpital Rule or Series Expansion
sin^n(x)=left(frace^ix-e^-ix2i ight)^n=frac1(2i)^nsum_k=0^ninom nke^i(2k-n)x=\ frac1(2i)^nsum_k=0^ninom nksum_j=0^inftyfraci^j(2k-n)^jj!x^j, và frac11-sin(x)=sum_n=0^inftyfrac1(2i)^nsum_k=0^ninom nksum_j=0^inftyfraci^j(2k-n)^jj!x^j. ...
The substitution seems unnecessary for this problem, but your intuition is right about using y = sin(x) should you have proceeded that way. Alternatively, you can complete the square sin^2(x)-2sin(x)+1 = 0 \ implies (sin(x)-1)^2=0 \ implies sin(x)-1 =0 \ implies sin(x) = 1 ...

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For domain: Denominator must not be equal to lớn 0, So, 2 - sin3x not=0 sin3x not=2, which is never possible as sin function varies from -1 khổng lồ 1 only. So, it can take any value of x. Therefore, ...
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left< eginarray l l 2 và 3 \ 5 và 4 endarray ight> left< eginarray l l l 2 và 0 và 3 \ -1 và 1 & 5 endarray ight>

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