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Step-by-step Solution

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

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Answer

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

Step-by-step explanation

Problem to solve:

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

First, factor the terms inside the radical for an easier handling

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

Taking the constant out of the radical

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

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Answer

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

Main topic:

Integration by trigonometric substitution

Used formulas:

8. See formulas

Time to solve it:

~ 1.23 seconds