Solve ∫ t/cscx wrt x

$$\int \frac { t } { \csc x } d x$$

Evaluate

$$-t\cos(x)+С$$

Solution Steps

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

$$t\int \sin(x)\mathrm{d}x$$

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

$$-t\cos(x)$$

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.

$$-t\cos(x)+С$$

Differentiate w.r.t. x

$$t\sin(x)$$