clear all;
%6_1
syms a t x
f1=sym('[a t^5;t*sin(x) log(x)]')
dfx=diff(f1,x)
dft2=diff(f1,t,2)
dfdt=diff(diff(f1,x),t)
%6_2
syms A a n x
dfdx=[A/(x-a) A/((x-1)^n);4/(x^3+4*x) 1/(5+4*sin(2*x))]
f2=int(dfdx)
f2_1=simple(f2);
f2_1
%6_3
syms w x
f3_1='2*sin(w)/w'
f3_2='sin(x/2)^6'
I_1=int(f3_1,w,0,inf)
I_2=int(f3_2,x,0,pi)
%6_4
syms A a s t
F4_1=laplace(A*exp(a*t))
f4_2=ilaplace(s/(s^2-1)^2)