What is the integral of e^ycos(x) ?

The integral of e^ycos(x) is e^ysin(x)+C

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integral of e^ycos(x)

\int e^{y} cos (x) d x

e^{y} sin (x) + C

Solution steps

\int e^{y} cos (x) d x

Take the constant out:

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

= e^{y} \cdot \int cos (x) d x

Use the common integral:

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

= e^{y} sin (x)

Add a constant to the solution

= e^{y} sin (x) + C

\frac{sin ( 2 x )}{2}

\int_{0}^{3} x^{2} - 2 x d x

\frac{d}{d x} ((2 - x)^{- 2})

y = \frac{x}{1 + x ^{2}}, (2, 0.4)

\frac{d y}{d x} = \frac{x ^{2} y ^{3}}{x + 3}