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I read another post Integral of the form, which shows the following indefinite integral

$\int \exp\left(-\frac{(a+bx)^2}{x}\right)\frac{dx}{\sqrt{x^3}} $

is solvable. Now, I'm wondering whether

$\int \exp\left(-\frac{(a+bx)^2}{x}\right)\frac{dx}{\sqrt{x}} $

can be solved too?

Is there anybody could give me a hint on that? Thanks a lot!

sty13 Y
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  • Have you actually tried to understand how was that integral solved? Where do you get stuck with this one? – Zacky Nov 25 '19 at 06:18
  • I think if this is a definite integral, the answers in that post gives a great idea and the definite integral version can be solved. I just got curious whether we can work out this indefinite integral. I didn't have wolfram...so I post this one. – sty13 Y Nov 25 '19 at 06:51
  • Maple says this here $$-{\frac {{{\rm e}^{b}}{x}^{3/2}\sqrt {\pi}}{\sqrt {{x}^{3}}\sqrt {a}} {\rm erf} \left({\frac {\sqrt {a}}{\sqrt {x}}}\right)} +C$$ – Dr. Sonnhard Graubner Nov 25 '19 at 06:53
  • This one is incorrect...anyway, thanks for your help. – sty13 Y Nov 25 '19 at 07:59
  • @Nyssa I might solve this one... still gets inspration from your previous post. It really helps. – sty13 Y Nov 25 '19 at 08:00

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