What is the integral of ysin(x) ?

The integral of ysin(x) is -ycos(x)+C

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integral of ysin(x)

\int y sin (x) d x

- y cos (x) + C

Solution steps

\int y sin (x) d x

Take the constant out:

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

= y \cdot \int sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= y (- cos (x))

Simplify

= - y cos (x)

Add a constant to the solution

= - y cos (x) + C

\int sec (x) (tan (x) + sec (x)) d x

\int \frac{1}{1 + e ^{2 x}} d x

y^{^{'}} = a y + b e^{- b}

\int \frac{e ^{x}}{( e ^{2 x} + 1 ) ( e ^{x} - 1 )} d x

y = \frac{4}{( 7 x ) ^{7}}