What is the integral of ((y^2)/2-ytan(x)) ?

The integral of ((y^2)/2-ytan(x)) is (y^2)/2 x+yln|cos(x)|+C

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

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

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

Solution steps

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

Apply the Sum Rule:

\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) ∣)

Simplify

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

Add a constant to the solution

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

\frac{9}{s ( s ^{2} + 9 s + 9 )}

y = (1 + 2 x)^{2}, at x = 1

\int \frac{1}{- 3 x ^{2} + 3 x + 7} d x

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

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

What is the integral of ((y^2)/2-ytan(x)) ?
The integral of ((y^2)/2-ytan(x)) is (y^2)/2 x+yln|cos(x)|+C