MATLAB: Can any one solve the Integration of following expression

integrationnumerical integration

integration of (x^a/(b+x))) or

integration of ((x/(b+x^a));

integration of (exp(x)/(b+exp(a*x));

integration of (exp(a*x)/(b+exp(x));

where, a and b are constants. x is variable. please find the solution for any one of the question.

Best Answer

The first one is

-x^a*(-1+LerchPhi(-x/b, 1, a)*a)/a

unless b = 0, and then it is (x^a)/a

The second one is

(1/2)*x^2*hypergeom([1, 2/a], [1+2/a], x^a*(-1)^csgn(I*x^a)/b)/b

if b < 0, and is

-x^2/((a-2)*x^a)

if b = 0, and is

(1/2)*x^2*hypergeom([1, 2/a], [1+2/a], -x^a/b)/b

if b > 0

Related Solutions

MATLAB: Needs derivative w.r.t. ‘ y ‘ & then graph w.r.t ‘ t ‘

diff is a function of the symbolic package, so when you try to derivate U, you are derivating a constant, and by a constant, so F is a 0. To do what you want, you should do it in symbolic and then replace your variable, like:

syms y t
P2=5;           
U=exp(y*sqrt(P2)).*(1-erf(y./(2.*sqrt(t))+ sqrt(P2.*t)));
S= - diff(U,y); 
v_t=0.01:0.01:5;
F = subs(S,y,0);
plot(v_t,vpa(subs(F,t,v_t)))
xlabel(' t');
ylabel('F');

MATLAB: How to solve this integration ???

This shows that MATLAB is not able to find a closed-form expression for the integration problem. You can still find the numerical answer by substituting the numeric values of a and b

syms x a b
c = (x*cos(x)*sin(x))/(a^2*cos(x)^2 + b^2*sin(x)^2)^2;
c_int = int(c, x, 0, pi/1);
x = subs(c_int, [a b], [1 2]);

This will give the value of integration at a=1, b=2. Result:

>> x
x =
-pi/12

Best Answer

Related Solutions

MATLAB: Needs derivative w.r.t. ‘ y ‘ & then graph w.r.t ‘ t ‘

MATLAB: How to solve this integration ???

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