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\int\frac{1}{\sqrt{1+4x^2}}dx

Integral of 1/((1+4x^2)^0.5)

Answer

$\frac{1}{2}\ln\left(2x+\sqrt{4x^2+1}\right)+C_0$

Step-by-step explanation

Problem

$\int\frac{1}{\sqrt{1+4x^2}}dx$
1

Primero factorizamos dentro del radical para reescribir los términos de una manera más cómoda

$\int\frac{1}{\sqrt{4\left(x^2+\frac{1}{4}\right)}}dx$

Unlock this step-by-step solution!

Answer

$\frac{1}{2}\ln\left(2x+\sqrt{4x^2+1}\right)+C_0$
$\int\frac{1}{\sqrt{1+4x^2}}dx$

Main topic:

Integration by trigonometric substitution

Used formulas:

8. See formulas

Time to solve it:

~ 1.54 seconds