Solve ∫ 1/vsqrt{u-1}dv

$$\int \frac { 1 } { v \sqrt { u - 1 } } d v$$

Evaluate

$$\frac{\ln(|v|)}{\sqrt{u-1}}+С$$

Solution Steps

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

$$\frac{\int \frac{1}{v}\mathrm{d}v}{\sqrt{u-1}}$$

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

$$\frac{\ln(|v|)}{\sqrt{u-1}}$$

If F\left(v\right) is an antiderivative of f\left(v\right), then the set of all antiderivatives of f\left(v\right) is given by F\left(v\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\frac{\ln(|v|)}{\sqrt{u-1}}+С$$

Differentiate w.r.t. v

$$\frac{1}{\sqrt{u-1}v}$$