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Question
I'm trying to Integrate 4x + 5 divided by sqrt 2x - 3 and have been given 2x - 3 = t^2 as the substitution. The answer is given as 2/3(2x-3)^3/2 + 11(2x-3)^1/2 + c. Have tryed everything but cannot relate to the 4x - 5. Some help or a direction to go would be greatly appreciated.
If you use the substitution t=2x-3 then dx=dt/2. & the integral
becomes : ∫(4x+5)/√(2x-3) dx = ∫[2(t+3)+5]/√t dt
=∫2t/√t dt + ∫11/√t dt = 2∫√t dt + 11∫dt/√t
=(2/3)[t]^(3/2) + (11/2)√t . Now lets substitute t=2x-3 we get :
=(2/3)(2x-3)^(3/2) + (11/2)(2x-3)^(1/2)
Alon.
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Answers by Expert:
Alon Mandes
Expertise
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
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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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