# Math Help - Integrating by eliminating square root

1. ## Integrating by eliminating square root

$\int_{\frac{{ - \pi }}
{4}}^{\frac{\pi }
{4}} {\sqrt {1 + {{\tan }^2}x} dx}
$

I'm not sure where to begin

2. Originally Posted by genlovesmusic09
$\int_{\frac{{ - \pi }}
{4}}^{\frac{\pi }
{4}} {\sqrt {1 + {{\tan }^2}x} dx}
$

I'm not sure where to begin
$sin^2x+cos^2x=1$

Let's divide by $cos^2x$

$tan^2x+1=sec^2x$

Can you take it from here?

3. $1 + {{\tan }^2}x = \sec^2x$

4. $\int {\sqrt {{{\sec }^2}x} dx = \int {\sqrt {\frac{{dx}}
{{{{\cos }^2}x}}} } }
$

i don't see the next step

5. Originally Posted by genlovesmusic09
$\int {\sqrt {{{\sec }^2}x} dx = \int {\sqrt {\frac{{dx}}
{{{{\cos }^2}x}}} } }
$

i don't see the next step
$\sqrt{(something)^2} = |something|
$

6. wow... i am overthinking
thanks