Symbolic Integration - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : System : Information : Updates : Maple 2015 : updates/Maple2015/Integration

Symbolic Integration

 

Indefinite integration

Definite integration

Indefinite integration

The capabilities of finding indefinite integrals in Maple have been improved. The following integrals could not be computed in previous versions of Maple. In particular, this applies to many integrands involving inverse hyperbolic functions, such as the following:

arcsinhxx ⅆx

12arcsinhx2+arcsinhxln1xx2+1+polylog2,x+x2+1+arcsinhxln1+x+x2+1+polylog2,xx2+1

(1.1)

ⅆⅆx

arcsinhxx2+1+ln1xx2+1x2+1+arcsinhx1xx2+11xx2+11+xx2+1ln1xx2+1x+x2+1+ln1+x+x2+1x2+1+arcsinhx1+xx2+11+x+x2+11xx2+1ln1+x+x2+1xx2+1

(1.2)

radnormal

arcsinhxx

(1.3)

arccothx3ⅆx

arccothx3x1+2arccothx33arccothx2ln11x1x+16arccothxpolylog2,1x1x+1+6polylog3,1x1x+13arccothx2ln1+1x1x+16arccothxpolylog2,1x1x+1+6polylog3,1x1x+1

(1.4)

radnormalⅆⅆx

arccothx3

(1.5)

arctanhtanhb x+a2x ⅆx

lnxarctanhtanhbx+a2+b2x2lnx32b2x22blnxarctanhtanhbx+ax+2barctanhtanhbx+ax

(1.6)

ⅆⅆx

arctanhtanhbx+a2x

(1.7)

Some other types of integrands are covered by the improvements as well.

lnx+an2x+b2ⅆx

lnx+an2x+b+2nlnx+anlnx+bab2nlnx+anlnx+aab2n2lnx+blnx+aabab2n2dilogx+aabab+n2lnx+a2ab

(1.8)

normalⅆⅆx

lnx+an2x+b2

(1.9)

More compact results

Some integrals that used to be expressed in terms of lengthy csgn expressions are now are given in more compact form.

x arctantanx3ⅆx

12x2arctantanx312x3arctantanx2+14x4arctantanx120x5

(1.1.1)

ⅆⅆx

xarctantanx3

(1.1.2)

Definite integration

Definite integrals can now also be computed for some non-smooth integrands, for which previous versions of Maple could only compute an indefinite integral.

∞∞x11/3x2+1ⅆx

3_R=RootOf23328_Z6+216_Z3+1_Rln6+_Rln216_R4_R3_R=RootOf23328_Z6+216_Z3+1_Rln6+_Rln216_R4+_R

(2.1)

radnormalevalcallvalues

1622/3π3+3

(2.2)