Solve ∫ ccosx/sin^2(w) wrt x

$$\int \frac { c \cos x } { \sin ^ { 2 } ( w ) } d x$$

Evaluate

$$\frac{c\sin(x)}{\left(\sin(w)\right)^{2}}+С$$

Solution Steps

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

$$\frac{c}{\left(\sin(w)\right)^{2}}\int \cos(x)\mathrm{d}x$$

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

$$\frac{c}{\left(\sin(w)\right)^{2}}\sin(x)$$

Simplify.

$$\frac{c\sin(x)}{\left(\sin(w)\right)^{2}}$$

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.

$$\begin{matrix}\frac{c\sin(x)}{\left(\sin(w)\right)^{2}}+С_{3},&\end{matrix}$$

Differentiate w.r.t. x

$$\frac{c\cos(x)}{\left(\sin(w)\right)^{2}}$$