[SOLVED] Help with trigonometric substitution

**vinson24** · March 19th 2010, 06:07 AM

$\int\ (dx/4+x^{2})^{2}$
dont know how to do this problem without the square root

**Prove It** · March 19th 2010, 06:08 AM

Originally Posted by vinson24

$\int\ (dx/4+x^{2})^{2}$
dont know how to do this problem without the square root

Are you sure it's not

$\int{\frac{dx}{(4 + x^2)^2}}$ ?

**vinson24** · March 19th 2010, 07:47 AM

Yes that's how you write it sorry

**skeeter** · March 19th 2010, 08:09 AM

$\int{\frac{dx}{(4 + x^2)^2}}$

$x = 2\tan{t}$

$dx = 2\sec^2{t} \, dt$

$\int \frac{2\sec^2{t}}{(4 + 4\tan^2{t})^2} \, dt$

$\frac{1}{8} \int \frac{\sec^2{t}}{(1 + \tan^2{t})^2} \, dt$

$\frac{1}{8} \int \frac{\sec^2{t}}{(\sec^2{t})^2} \, dt$

$\frac{1}{8} \int \frac{1}{\sec^2{t})} \, dt$

$\frac{1}{8} \int \cos^2{t} \, dt$

take it from here?

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