Integration...Please check my solution

Mar 2010
6
0
Hi ,
Could you please help me with Integration : [sec sqrt(x)]^2 / 2 sqrt (x) ( 1+[tan sqrt(x)]^2]

First i simplified it :
sec sqrt(x)]^2 is equivalent to 1+[tan sqrt(x)]^2] I cancel them out.
1/2 sqrt(x) would remain.
Then the integration is equal to :
1/2 Integral x^ -1/2
The final answer is :
( x^1/2)
Please let me know if my answer is correct.
I would really appreciate it if you show me the correct solution.
 

Soroban

MHF Hall of Honor
May 2006
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Lexington, MA (USA)
Hello, alireza64851

\(\displaystyle \int \frac{\sec^2\!\sqrt{x} }{2\sqrt{x}(1+\tan^2\!\sqrt{x})}\,dx \)


First i simplified it :

. . \(\displaystyle \sec^2\!\sqrt{x} \:=\:1+\tan^2\!\sqrt{x}\) . . . I cancelled them out.

Then: .\(\displaystyle \frac{1}{2\sqrt{x}}\) would remain.

Then the integration is equal to: .\(\displaystyle \tfrac{1}{2}\int x^{-\frac{1}{2}}dx\)

The final answer is: .\(\displaystyle x^{\frac{1}{2}} + C\)

Please let me know if my answer is correct.

Absolutely correct! . . . Nice work!