Integration

 

In Reduce

For comparison with other CAS choose from: Axiom Derive Macsyma Maple Mathematica

inputs outputs

    int(x**2*(a+b*x)**p,x);

              p     3      2            2  2  2      2    2    3  2  3
    ((a + b*x) *(2*a  - 2*a *b*p*x + a*b *p *x  + a*b *p*x  + b *p *x

                       3    3      3  3     3   3      2
                  + 3*b *p*x  + 2*b *x ))/(b *(p  + 6*p  + 11*p + 6))

    int(x**2*log(x**2+a**2),x);

                x    3          2    2   3      2        3
      - 6*atan(---)*a  + 3*log(a  + x )*x  + 6*a *x - 2*x
                a
    -------------------------------------------------------
                               9

    int(x*d**x*sin x,x);

      x               3                  2
    (d *(sin(x)*log(d) *x - sin(x)*log(d)  + sin(x)*log(d)*x + sin(x)

                         2                                         4
          - cos(x)*log(d) *x + 2*cos(x)*log(d) - cos(x)*x))/(log(d)

                  2
        + 2*log(d)  + 1)

    int(x*sqrt(a+b*x)**p,x);

                p/2        2              2    2      2  2
     2*(a + b*x)   *( - 2*a  + a*b*p*x + b *p*x  + 2*b *x )
    --------------------------------------------------------
                        2   2
                       b *(p  + 6*p + 8)

    int(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
      x        3    x                       2            2
    (e  *log(x)  + e  *log(x)*x + log(log(x)  + x)*log(x)

                  2                         2
      + log(log(x)  + x)*x - log(x))/(log(x)  + x)