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How can we plot this integration for m=1,\theta = 0.2? Here r_h(lower limit) = 1.

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  • $\begingroup$ Please enter your expressions in correctly formatted, copy-and-pasteable Mathematica code. $\endgroup$ – march Jul 7 '16 at 17:05
  • $\begingroup$ NIntegrate[] could be used, but a faster way would be to formulate the equivalent ODE and use NDSolve[]. $\endgroup$ – J. M. will be back soon Jul 7 '16 at 17:06
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    $\begingroup$ Per @J.M.'s comment, see for instance this answer. $\endgroup$ – march Jul 7 '16 at 17:07
  • $\begingroup$ t = \!( *SubsuperscriptBox[([Integral]), (1), (r)](1/((1 - 4\ m\ /((r [Sqrt][Pi])) {GammaRegularized[3/2, r^2/((4 [Theta]))]})) [DifferentialD]r)) $\endgroup$ – Emlie Jul 7 '16 at 17:07
  • $\begingroup$ Put the code in your question, please; however, Copy As > Input Text would be much better for you and for us. $\endgroup$ – J. M. will be back soon Jul 7 '16 at 17:10
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Just picking up the idea mentioned in the comments, your code would be

f[r_] := 1/(1 - 4/(r*Sqrt[Pi])*Gamma[1.5, r^2/(4*0.2)])
F[y_?NumericQ] := NIntegrate[f[r], {r, 1, y}]

LogLogPlot[F[r], {r, 1, 100}]
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