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Calculus/Finding antiderivative

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Expert: Alon Mandes - 2/7/2010


Question
can u help me find the antiderivative of this:

(sec˛x)/(4-tan˛x)^3/2 dx

Answer
The derivative of f/g^(3/2) is :
f'*g^(3/2)-f*(3/2)*g'*g^(1/2)
------------------------- .
     g^3

In our case :
f=sec˛(x) Therefore f'=2sec(x)*sec(x)tan(x)
g=4-tan˛(x) Therefore : g'=-2tan(x)*sec˛(x)
Hence,
The total derivative will be :

2sec(x)*sec(x)tan(x)*(4-tan˛x)^(3/2)-sec˛(x)*(3/2)*[-2tan(x)*sec˛(x)]*(4-tan˛x)^(1/2)
--------------------------------------------------------------------------------------
     (4-tan˛x)^3

I will leave it for you, to simplify the form .

Alon.

Calculus

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Alon Mandes

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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

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1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

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M.A in Mathematics & Bs.c in Electronics.

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