Question

如何用matlab计算sinxdx

Answer 1

∫1/ sinxdx

=∫cscxdx

=ln|cscx-cotx|+C

=ln|tan(x/2)|+C

具体计算步骤如下：

附：LATEX代码

&\int \frac{dx}{\sin x} 

=\int \frac{dx}{2\sin\frac{x}{2}\cos\frac{x}{2}  }\\

=&\int \frac{dx}{2\tan\frac{x}{2}\cos^2\frac{x}{2}  }  

=\int\frac{d\left ( \tan\frac{x}{2}  \right ) }{\tan\frac{x}{2} } \\

=&\ln \left |\tan\frac{x}{2} \right |+C  =\ln \left |\frac{\sin\frac{x}{2}  }{\cos\frac{x}{2} } \right |  +C\\

=&\ln \left |\frac{2\sin^2\frac{x}{2} }{\sin x}\right |+C=\ln\left |\frac{1-\cos x}{\sin x}   \right | +C\\

=&\ln|\csc x -\cot x|+C