I = ∫1/√(x^2+2x+10) dx I = ∫1/√((x+1)^2+9) dx I = ∫1/√((x+1)^2+3^2) dx ∫1/√(x^2+a^2) dx #160; #160; = m (x+√(x^2+a^2))+c I = ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Integration of Irrational Algebraic Fractions - 2

Solve ∫dx√x2...

Question

Solve
$\int \frac{d x}{\sqrt{x^{2} + 2 x + 10}}$

Open in App

Solution

$I = \int \frac{1}{\sqrt{x^{2} + 2 x + 10}}$ dx
$I = \int \frac{1}{\sqrt{(x + 1)^{2} + 9}}$ dx
$I = \int \frac{1}{\sqrt{(x + 1)^{2} + 3^{2}}}$ dx
$\int \frac{1}{\sqrt{x^{2} + a^{2}}}$ dx $= m (x + \sqrt{x^{2} + a^{2}}) + c$
$I = m [(x + 1) + \sqrt{x^{2} + 2 x + 10}] + c$

Suggest Corrections