Solve ∫ sqrt{169+x/x wrt x

$$\int{ \sqrt{ \frac{ 169+x }{ x } } }d x$$

Evaluate

$$-\frac{169\ln(-\frac{\left(-\sqrt{\frac{x+169}{x}}+1\right)|\frac{-\sqrt{\frac{x+169}{x}}+1}{\sqrt{\frac{x+169}{x}}}|\left(x+169\right)}{169\sqrt{\frac{x+169}{x}}})}{2}+\sqrt{\frac{x+169}{x}}x+С$$

$$x<-169\text{ or }x>0$$

Differentiate w.r.t. x

$$\frac{4|\frac{-\sqrt{\frac{x+169}{x}}+1}{\sqrt{\frac{x+169}{x}}}|x\left(\sqrt[3]{x}\left(x+169\right)\right)^{\frac{3}{2}}\sqrt{\left(x+169\right)x^{3}}+676|\frac{-\sqrt{\frac{x+169}{x}}+1}{\sqrt{\frac{x+169}{x}}}|\left(\sqrt[3]{x}\left(x+169\right)\right)^{\frac{3}{2}}\sqrt{\left(x+169\right)x^{3}}+169|\frac{-\sqrt{\frac{x+169}{x}}+1}{\sqrt{\frac{x+169}{x}}}|x^{2}|x\left(x+169\right)|-338\sqrt{\frac{x+169}{x}}|\frac{-\sqrt{\frac{x+169}{x}}+1}{\sqrt{\frac{x+169}{x}}}|x^{2}\left(\sqrt[3]{x}\left(x+169\right)\right)^{\frac{3}{2}}-169|\frac{-\sqrt{\frac{x+169}{x}}+1}{\sqrt{\frac{x+169}{x}}}|x^{2}\sqrt{\left(x+169\right)x^{3}}+28561|\frac{-\sqrt{\frac{x+169}{x}}+1}{\sqrt{\frac{x+169}{x}}}|x|x\left(x+169\right)|-28561sign(\frac{-\sqrt{\frac{x+169}{x}}+1}{\sqrt{\frac{x+169}{x}}})x|x\left(x+169\right)|-28561|\frac{-\sqrt{\frac{x+169}{x}}+1}{\sqrt{\frac{x+169}{x}}}|x\sqrt{\left(x+169\right)x^{3}}}{4|\frac{-\sqrt{\frac{x+169}{x}}+1}{\sqrt{\frac{x+169}{x}}}|x\left(\sqrt[3]{x}\left(x+169\right)\right)^{\frac{3}{2}}|x\left(x+169\right)|}$$

$$x<-169\text{ or }x>0$$