Asked by mathemagician
                Integrate : (x^3)dx/sqrt. of (3x^2 - 5)
Let x=sqrt(5/3)secant theta
dx=sqrt(5/3)secant theta tangent theta
Sqrt. (3x^2-5) = sqrt. (5/3) tangent theta
            
            
        Let x=sqrt(5/3)secant theta
dx=sqrt(5/3)secant theta tangent theta
Sqrt. (3x^2-5) = sqrt. (5/3) tangent theta
Answers
                    Answered by
            Steve
            
    ∫ x^3/√(3x^2-5) dx
x = √(5/3) secθ
3x^2-5 = 5tan^2θ
dx = √(5/3) secθ tanθ dθ
and the integral becomes
∫ √(5/3)^3 sec^3θ/(√5 tanθ) √(5/3) secθ tanθ dθ
= 5/9 √5 ∫sec^4θ dθ
That one's not so hard, eh?
    
x = √(5/3) secθ
3x^2-5 = 5tan^2θ
dx = √(5/3) secθ tanθ dθ
and the integral becomes
∫ √(5/3)^3 sec^3θ/(√5 tanθ) √(5/3) secθ tanθ dθ
= 5/9 √5 ∫sec^4θ dθ
That one's not so hard, eh?
                                                    There are no AI answers yet. The ability to request AI answers is coming soon!
                                            
                Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.