integral of ((y^2)/2-ytan(x))

解答

\int (\frac{y ^{2}}{2} - y tan (x)) d x

\frac{y ^{2}}{2} x + y ln ∣ cos (x) ∣ + C

求解步骤

\int \frac{y ^{2}}{2} - y tan (x) d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{y ^{2}}{2} d x - \int tan (x) y d x

\int \frac{y ^{2}}{2} d x = \frac{y ^{2}}{2} x

\int tan (x) y d x = - y ln ∣ cos (x) ∣

= \frac{y ^{2}}{2} x - (- y ln ∣ cos (x) ∣)

化简

= \frac{y ^{2}}{2} x + y ln ∣ cos (x) ∣

解答补常数

= \frac{y ^{2}}{2} x + y ln ∣ cos (x) ∣ + C

in v erse l a pl a ce \frac{9}{s ( s ^{2} + 9 s + 9 )}

t an g e n t y = (1 + 2 x)^{2}, at x = 1

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x \to 2 lim (\frac{1}{2 ( x - 2 )})

\int \frac{1}{5 - 4 x - x ^{2}} d x