integral of (cos^4(x))/(sin^2(x))

解答

\int \frac{cos ^{4} ( x )}{sin ^{2} ( x )} d x

- cos^{4} (x) cot (x) - 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x))) + C

求解步骤

\int \frac{cos ^{4} ( x )}{sin ^{2} ( x )} d x

使用分布积分法

= - cos^{4} (x) cot (x) - \int 4 cos^{3} (x) sin (x) cot (x) d x

\int 4 cos^{3} (x) sin (x) cot (x) d x = 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x)))

= - cos^{4} (x) cot (x) - 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x)))

解答补常数

= - cos^{4} (x) cot (x) - 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x))) + C

in v erse l a pl a ce \frac{( s ^{2} )}{s ^{3} - 1}

\frac{\partial}{\partial x} (e^{- (x^{2} + y^{2})})

x \to 8 lim (x - 2)

x \to 2 lim (\frac{7}{( x - 2 ) ^{2}})

cos (x) y^{^{'}} + sin (x) y = 2 cos^{3} (x) sin (x) - 1