Solve ∫ wrt y/7y

$$\int \frac { d y } { 7 y }$$

Evaluate

$$\frac{\ln(|y|)}{7}+С$$

Solution Steps

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

$$\frac{\int \frac{1}{y}\mathrm{d}y}{7}$$

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

$$\frac{\ln(|y|)}{7}$$

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.

$$\frac{\ln(|y|)}{7}+С$$

Differentiate w.r.t. y

$$\frac{1}{7y}$$