Integration

 

In Macsyma

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

inputs outputs

    integrate(x^2*(a+b*x)^p, x);

  3   2             3      2   2       2      2            3    p log(b x + a)
(b  (p  + 3 p + 2) x  + a b  (p  + p) x  - 2 a  b p x + 2 a ) %e
                           3   3      2
                          b  (p  + 6 p  + 11 p + 6)

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

                                                    3      2
                                       3      x    x  - 3 a  x
                  3      2    2    2 (a  atan(-) + -----------)
                 x  log(x  + a )              a         3
                 --------------- - ----------------------------
                        3                       3

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

       3                     2           log(d) x
 (((log (d) + log(d)) x - log (d) + 1) %e         sin(x)

          2                         log(d) x             4           2
 + ((- log (d) - 1) x + 2 log(d)) %e         cos(x))/(log (d) + 2 log (d) + 1)

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

                                                    p log(b x + a)
                                                    --------------
               2            2                  2          2
             (b  (2 p + 4) x  + 2 a b p x - 4 a ) %e
             -----------------------------------------------------
                                2   2
                               b  (p  + 6 p + 8)

    radcan(%);

                       p/2      2        2   2                  2
              (b x + a)    ((2 b  p + 4 b ) x  + 2 a b p x - 4 a )
              ----------------------------------------------------
                              2  2      2        2
                             b  p  + 6 b  p + 8 b

    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             log(x)        x
                  log(log (x) + x) - ----------- + %e   log(x)
                                        2
                                     log (x) + x