$\int {x^n dx \over z^m} = {x^{n-2} \over {z^{m-1}(n+1-3m)b}}+{(n-2)a \over {b(n+1-3m)}}{\int {x^{n-3} dx \over z^m}}$

here $z = a+ bx^3$

what is the idea to prove this equation by doing integration? I tried integration by parts.


closed as off-topic by heropup, TheSimpliFire, José Carlos Santos, Shailesh, Mohammad Riazi-Kermani Mar 4 '18 at 0:17

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  • 2
    $\begingroup$ I down vote this now, because you have several similar questions recently, and they all work more or less the same. $\endgroup$ – mickep Mar 3 '18 at 18:44
  • $\begingroup$ Yes, you are right! but please help me to understand this problem. $\endgroup$ – Atiqur Rahman Mar 3 '18 at 19:01
  • $\begingroup$ You do know that it will be integration by parts, followed by a bit of linear algebra ? Add this context to your question. & maybe tell us that you do not know where to start the integration by parts. $\endgroup$ – Donald Splutterwit Mar 3 '18 at 19:46
  • $\begingroup$ Yes, You are right. I do not understand where to start the integration by parts. $\endgroup$ – Atiqur Rahman Mar 3 '18 at 21:11
  • $\begingroup$ It is important to add a comment like this into question; it will add context. Make reference to some of your previous questions; explain you understand the idea that the solution will involve integration by parts & some imaginative linear algebra. Make your next question more about the underlying philosophy that is required to solve these types of problems & how to initiate the integration by part, rather than a "do this specific integral for me". Understanding all the formulea in G&R is a noble quest & I wish you the best of luck $\ddot \smile$ $\endgroup$ – Donald Splutterwit Mar 3 '18 at 21:56

Integrate by parts \begin{eqnarray*} \int \color{blue}{\frac{3(m-1)bx^2}{(a+bx^3)^m}} \color{red}{x^{n-2}} dx \end{eqnarray*} I leave you to do the linear algebra.


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