PatrickT

Dr. Patrick T

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16 years, 305 days

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These are replies submitted by PatrickT

then select the url obtained after the upload and insert that into the appropriate box. You may also want to select a width of about 500 for your figure, otherwise it may too wide or too narrow.

Maple is not really for a one off use. I also get frustrated when I try to use "internet explorer", which is supposed to be easy to use, but you'll find that those who find it easy to use do so because they use it a lot, not because it is easy the first time around -- few softs are.

then select the url obtained after the upload and insert that into the appropriate box. You may also want to select a width of about 500 for your figure, otherwise it may too wide or too narrow.

Maple is not really for a one off use. I also get frustrated when I try to use "internet explorer", which is supposed to be easy to use, but you'll find that those who find it easy to use do so because they use it a lot, not because it is easy the first time around -- few softs are.

oops, thanks for pointing that out Alejandro, I copy-pasted the OP's integrand without paying much attention to it, just changing the square brackets, but in my haste failed to spot that ^ was intended to apply to 1/2. There seem to be no closed-form solutions when the square root is taken into account.

OP's integrand: [exp(-cx)]/[a^2+x^2]^1/2

oops, thanks for pointing that out Alejandro, I copy-pasted the OP's integrand without paying much attention to it, just changing the square brackets, but in my haste failed to spot that ^ was intended to apply to 1/2. There seem to be no closed-form solutions when the square root is taken into account.

OP's integrand: [exp(-cx)]/[a^2+x^2]^1/2

algcurves[plot_real_curve] is very nice, I could work out how to control the color of the line but not of the green points,

algcurves[plot_real_curve](z1,c,z,axes=box,labels=[c,z],colorOfCurve=black);

algcurves[plot_real_curve] is very nice, I could work out how to control the color of the line but not of the green points,

algcurves[plot_real_curve](z1,c,z,axes=box,labels=[c,z],colorOfCurve=black);

The content of this post could usefully be part of Joe Riel's suggestion on mapleprimes FGAs:

http://www.mapleprimes.com/forum/suggestionfrequentanswersection

The following discussion may be relevant too:

http://www.mapleprimes.com/forum/matrixcontainingvaluesfxylistxy

The content of this post could usefully be part of Joe Riel's suggestion on mapleprimes FGAs:

http://www.mapleprimes.com/forum/suggestionfrequentanswersection

The following discussion may be relevant too:

http://www.mapleprimes.com/forum/matrixcontainingvaluesfxylistxy

expr := (exp(-c*x))/(a^2+b*x^2)^1/2;
int( expr, x ) assuming c::posint;
                                    exp(-c x)
                        expr := 1/2 ---------
                                     2      2
                                    a  + b x


               /                                1/2
           1/2 |        c a            -c x (-b)    + c a
  -1/4 (-b)    |exp(- -------) Ei(1, - ------------------)
               |          1/2                   1/2
               \      (-b)                  (-b)

                                         1/2       \
                 c a            -c x (-b)    - c a |
         - exp(-------) Ei(1, - ------------------)|/(b a)
                   1/2                   1/2       |
               (-b)                  (-b)          /

expr := (exp(-c*x))/(a^2+b*x^2)^1/2;
int( expr, x ) assuming c::posint;
                                    exp(-c x)
                        expr := 1/2 ---------
                                     2      2
                                    a  + b x


               /                                1/2
           1/2 |        c a            -c x (-b)    + c a
  -1/4 (-b)    |exp(- -------) Ei(1, - ------------------)
               |          1/2                   1/2
               \      (-b)                  (-b)

                                         1/2       \
                 c a            -c x (-b)    - c a |
         - exp(-------) Ei(1, - ------------------)|/(b a)
                   1/2                   1/2       |
               (-b)                  (-b)          /

int( expr, x ) assuming c::posint;
  -1/4 I (exp(c a I) Ei(1, c x + c a I)

         - exp(-I c a) Ei(1, c x - c a I))/a

int( expr, x ) assuming c::posint;
  -1/4 I (exp(c a I) Ei(1, c x + c a I)

         - exp(-I c a) Ei(1, c x - c a I))/a

Are you sure you NEED the antiderivative? perhaps you just need the integral between 0 and 1 or between 0 and infinity, for instance.

closed-forms for the antiderivative exist for specific values of a, keeping c symbolic, e.g.

 

int( eval(expr,{a=0}), x);

                          /exp(-c x)             \
                   -1/2 c |--------- - Ei(1, c x)|
                          \   c x                /

int( eval(expr,{a=1}), x);

  -1/2 (1/2 I c exp(c I) Ei(1, c x + c I)

         - 1/2 I c exp(-I c) Ei(1, c x - c I))/c

Are you sure you NEED the antiderivative? perhaps you just need the integral between 0 and 1 or between 0 and infinity, for instance.

closed-forms for the antiderivative exist for specific values of a, keeping c symbolic, e.g.

 

int( eval(expr,{a=0}), x);

                          /exp(-c x)             \
                   -1/2 c |--------- - Ei(1, c x)|
                          \   c x                /

int( eval(expr,{a=1}), x);

  -1/2 (1/2 I c exp(c I) Ei(1, c x + c I)

         - 1/2 I c exp(-I c) Ei(1, c x - c I))/c

that was quick -- hopefully the captcha is not something a robot can figure out!

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