integral of 1/((sin(a)y)(cos(a)y))

解答

\int \frac{1}{( sin ( a ) y ) ( cos ( a ) y )} d y

- \frac{1}{y sin ( a ) cos ( a )} + C

求解步骤

\int \frac{1}{sin ( a ) y cos ( a ) y} d y

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{sin ( a ) cos ( a )} \cdot \int \frac{1}{yy} d y

yy = y^{2}

= \frac{1}{sin ( a ) cos ( a )} \cdot \int \frac{1}{y ^{2}} d y

使用幂法则

= \frac{1}{sin ( a ) cos ( a )} (- \frac{1}{y})

化简

\frac{1}{sin ( a ) cos ( a )} (- \frac{1}{y}) : - \frac{1}{y sin ( a ) cos ( a )}

= - \frac{1}{y sin ( a ) cos ( a )}

解答补常数

= - \frac{1}{y sin ( a ) cos ( a )} + C

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