What is the integral of y-e^{cos(x)}sin(x) ?

The integral of y-e^{cos(x)}sin(x) is yx+e^{cos(x)}+C

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integral of y-e^{cos(x)}sin(x)

\int y - e^{c o s (x)} sin (x) d x

y x + e^{c o s (x)} + C

Solution steps

\int y - e^{c o s (x)} sin (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 y d x - \int sin (x) e^{c o s (x)} d x

\int y d x = y x

\int sin (x) e^{c o s (x)} d x = - e^{c o s (x)}

= y x - (- e^{c o s (x)})

Simplify

= y x + e^{c o s (x)}

Add a constant to the solution

= y x + e^{c o s (x)} + C

\int \frac{( 3 x - 5 )}{x ^{3} - 5 x ^{2} - 14 x} d x

\frac{d}{d x} (3 x^{3} + y^{3})

(x cos (x))^{^{'}}

\int cos (x) sec^{2} (x) d x

f (x) = - sec^{2} (x)

What is the integral of y-e^{cos(x)}sin(x) ?
The integral of y-e^{cos(x)}sin(x) is yx+e^{cos(x)}+C