How to Integrate (Tanx)^(1/2)?

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In summary, the person from Iran is struggling with finding the integral of (Tanx)^(1/2) and has been working on it for several hours with no progress. They ask for help and are advised to set u=sqrt(tan x) and integrate with respect to u. They are then asked to show some of their work and to specify their understanding and level of progress. They are also given the hint that x^4 + 1 = (x^2+1)^2- (x\sqrt{2})^2.
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Homework Statement


hey guys.
im from Iran and i can't speak En professionally.
I have a question about integral and it is integral of (Tanx)^(1/2).
my calculation took several hours but I did not have any progres in the calculation.
Would someone help me to solve this math problem?
Thanks.

Homework Equations


(tanx)^(1/2)

The Attempt at a Solution


integral of (Tanx)^(1/2)
 
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  • #2
Hey,

Can you maybe specify your domain of integration and also show some of the work you have already done.
 
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  • #3
Try setting u=sqrt(tan x) and integrating with respect to u
 
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  • #4
can u explain how to solve the problem after setting u=tanx and du=(1+tanx^2)du?
 
  • #5
No I said try u=sqrt(tan x) so that u^2 = tan x

Can you show some work? we don't know what you've tried and we don't know your level of understanding.
 
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  • #6
and after u^2=tan x as usual Distinguish from Equality?
and by it can i solve this problem?
 
  • #7
This integral is horrendously tedious. It might help to know that [itex] x^4 + 1 = (x^2+1)^2- (x\sqrt{2})^2 [/itex]
 
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FAQ: How to Integrate (Tanx)^(1/2)?

What is the integral of (tanx)^(1/2)?

The integral of (tanx)^(1/2) is equal to 2/3(tanx)^(3/2) + C, where C is the constant of integration.

How do you solve the integral of (tanx)^(1/2)?

To solve the integral of (tanx)^(1/2), you can use the substitution method by letting u = tanx and du = sec^2(x)dx. This will result in the integral becoming 1/2 ∫ u^(-1/2) du, which can then be solved using the power rule.

Can the integral of (tanx)^(1/2) be simplified further?

Yes, the integral of (tanx)^(1/2) can be simplified further by using trigonometric identities. For example, you can rewrite tanx as sinx/cosx and then use the power reduction formula for the sine function to simplify the integral.

What is the domain of the integral of (tanx)^(1/2)?

The domain of the integral of (tanx)^(1/2) is all real numbers except for values of x where tanx is undefined, such as x = (2n+1)π/2, where n is an integer.

Can the integral of (tanx)^(1/2) be used to find the area under a curve?

Yes, the integral of (tanx)^(1/2) can be used to find the area under a curve. However, since tanx has vertical asymptotes, the area may be limited and may require additional techniques, such as breaking up the integral into smaller intervals or using the limit definition of the integral.

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