Solve ∫ cos(1/t)/t^2

$$\int \frac { \cos ( 1 / t ) } { t ^ { 2 } }$$

Evaluate

$$\frac{x\cos(\frac{1}{t})}{t^{2}}+С$$

Solution Steps

Find the integral of \frac{\cos(\frac{1}{t})}{t^{2}} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{\cos(\frac{1}{t})}{t^{2}}x$$

Simplify.

$$\frac{\cos(\frac{1}{t})x}{t^{2}}$$

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.

$$\frac{\cos(\frac{1}{t})x}{t^{2}}+С$$

Differentiate w.r.t. x

$$\frac{\cos(\frac{1}{t})}{t^{2}}$$