Solve ∫ e^siny wrt x

$$\int e ^ { \sin y } d x$$

Evaluate

$$xe^{\sin(y)}+С$$

Solution Steps

Find the integral of e^{\sin(y)} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$e^{\sin(y)}x$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$e^{\sin(y)}x+С$$

Differentiate w.r.t. x

$$e^{\sin(y)}$$