integrals exponencials

∫ [e^{( f(x) )^{n}}] d[x] = e^{( f(x) )^{n}} [o(x)o] ( ( f(x) )^{n} )^{[o(x)o](-1)}


∫ [e^{( ax )^{n}}] d[x] = ...
...e^{( ax )^{n}} [o(x)o] (1/a^{2})·(1/n)·( 1/((-n)+2) )·( ( ax )^{(-n)+2} )


∫ [e^{( ax^{2}+bx )^{n}}] d[x] = ...
...e^{( ax^{2}+bx )^{n}} [o(x)o]...
...(1/n)·( 1/((-n)+2) )·( ( ax^{2}+bx )^{(-n)+2} ) [o(x)o] (1/2a)·(-1)·( 2ax+b )^{(-1)}


∫ [e^{( ax^{3}+bx^{2}+cx )^{n}}] d[x] = ...
...e^{( ax^{3}+bx^{2}+cx )^{n}} [o(x)o]...
...(1/n)·( 1/((-n)+2) )·( ( ax^{3}+bx^{2}+cx )^{(-n)+2} ) [o(x)o] ...
...(-1)·( 3ax^{2}+2bx+c )^{(-1)} [o(x)o] (1/6a)·ln(6ax+b)


∫ [e^{( ax^{4}+bx^{3}+cx^{2}+dx )^{n}}] d[x] = ...
...e^{( ax^{4}+bx^{3}+cx^{2}+dx )^{n}} [o(x)o]...
...(1/n)·( 1/((-n)+2) )·( ( ax^{4}+bx^{3}+cx^{2}+dx )^{(-n)+2} ) [o(x)o] ...
...(-1)·( 4ax^{3}+3bx^{2}+2cx+d )^{(-1)} [o(x)o] ln(12ax^{2}+6bx+2c) [o(x)o] (1/24a)·ln(24ax+6b)