Solve ∫ 3cosx-1/x

$$\int 3 \cos x - 1 / x$$

Evaluate

$$-\ln(|x|)+3\sin(x)+С$$

Solution Steps

Integrate the sum term by term.

$$\int 3\cos(x)\mathrm{d}x+\int -\frac{1}{x}\mathrm{d}x$$

Factor out the constant in each of the terms.

$$3\int \cos(x)\mathrm{d}x-\int \frac{1}{x}\mathrm{d}x$$

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

$$3\sin(x)-\int \frac{1}{x}\mathrm{d}x$$

Use \int \frac{1}{x}\mathrm{d}x=\ln(|x|) from the table of common integrals to obtain the result.

$$3\sin(x)-\ln(|x|)$$

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.

$$3\sin(x)-\ln(|x|)+С$$

Differentiate w.r.t. x

$$3\cos(x)-\frac{1}{x}$$