Solve ∫ e^-xsiny wrt y

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

Evaluate

$$-\frac{\cos(y)}{e^{x}}+С$$

Solution Steps

Factor out the constant using \int af\left(y\right)\mathrm{d}y=a\int f\left(y\right)\mathrm{d}y.

$$\frac{\int \sin(y)\mathrm{d}y}{e^{x}}$$

Use \int \sin(x)\mathrm{d}x=-\cos(x) from the table of common integrals to obtain the result.

$$-\frac{\cos(y)}{e^{x}}$$

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

$$-\frac{\cos(y)}{e^{x}}+С$$

Differentiate w.r.t. x

$$\frac{\cos(y)}{e^{x}}$$