Integrace

In Axiom

Pro srovnani s jinymi CAS zvolte Derive Macsyma Maple Mathematica Reduce integrate(x**2*(a+b*x)**p, x)

   3 2     3      3  3       2 2      2   2     2          3   p log(b x + a)
((b p  + 3b p + 2b )x  + (a b p  + a b p)x  - 2a b p x + 2a )%e
                          3 3     3 2      3      3
                         b p  + 6b p  + 11b p + 6b
                                          Type: Union(Expression Integer,...)

integrate(x**2*log(x**2+a**2), x)

      3     2    2      3       x      3     2
    3x log(x  + a ) + 6a atan(- -) - 2x  + 6a x
                                a
                         9
                                          Type: Union(Expression Integer,...)

integrate(x*d**x*sin x, x)

                  3         2                                       2
         (x log(d)  - log(d)  + x log(d) + 1)sin(x) - x cos(x)log(d)
       +
         2cos(x)log(d) - x cos(x)
    *
         x log(d)
       %e
  /
           4          2
     log(d)  + 2log(d)  + 1
                                          Type: Union(Expression Integer,...)

integrate(x*sqrt(a+b*x)**p, x)

                                              +-------+
        2      2  2                2   p log(\|b x + a )
    ((2b p + 4b )x  + 2a b p x - 4a )%e
                      2 2     2      2
                     b p  + 6b p + 8b
                                          Type: Union(Expression Integer,...)

integrate(2*x*%e**(x**2)*log(x)+%e**(x**2)/x+(log(x)-2)/(log(x)**2+x)**2+ _

((2/x)*log(x)+(1/x)+1)/(log(x)**2+x), x)

                                       2                2
           2               2          x       3        x
    (log(x)  + x)log(log(x)  + x) + %e  log(x)  + (x %e   - 1)log(x)
                                    2
                              log(x)  + x
                                          Type: Union(Expression Integer,...)