integrals: sinus y cosinus

int[ ( sin(x) )^{n} ] d[x] = ...

... (1/(n+1))·( sin(x) )^{n+1} [o(x)o] ( sin(x)+( x [o(x)o] ln( cos(x) ) [o(x)o] cos(x) ) )

int[ ( cos(x) )^{n} ] d[x] = ...

... (1/(n+1))·( cos(x) )^{n+1} [o(x)o] ( cos(x)+( (-x) [o(x)o] ln( sin(x) ) [o(x)o] sin(x) ) )

int[ ( sin(ax+b) )^{n} ] d[x] = ...

... (1/(n+1))·( sin(ax+b) )^{n+1} [o(x)o] ...

... ( sin(ax+b)+( (1/a)·x [o(x)o] ln( cos(ax+b) ) [o(x)o] cos(ax+b) ) ) [o(x)o] (1/a^{2})·x

int[ ( cos(ax+b) )^{n} ] d[x] = ...

... (1/(n+1))·( cos(ax+b) )^{n+1} [o(x)o] ...

... ( cos(ax+b)+( (1/a)·(-x) [o(x)o] ln( sin(ax+b) ) [o(x)o] sin(ax+b) ) ) [o(x)o] (1/a^{2})·x

int[ ( sin(ax^{2}+bx+c) )^{n} ] d[x] = ...

... (1/(n+1))·( sin(ax^{2}+bx+c) )^{n+1} [o(x)o] ...

... ( ...

... sin(ax^{2}+bx+c)+...

... ( ... 

... (1/(2a))·x [o(x)o] ln(2ax+b) [o(x)o] ...

... ln( cos(ax^{2}+bx+c) ) [o(x)o] cos(ax^{2}+bx+c) ...

... ) ...

... ) ...

... [o(x)o] ...

... (2ax+b)^{(-1)} [o(x)o] (1/(2a))·(-x)

int[ ( cos(ax^{2}+bx+c) )^{n} ] d[x] = ...

... (1/(n+1))·( cos(ax^{2}+bx+c) )^{n+1} [o(x)o] ...

... ( ...

... cos(ax^{2}+bx+c)+...

... ( ... 

... (1/(2a))·(-x) [o(x)o] ln(2ax+b) [o(x)o] ...

... ln( sin(ax^{2}+bx+c) ) [o(x)o] sin(ax^{2}+bx+c) ...

... ) ...

... ) ...

... [o(x)o] ...

... (2ax+b)^{(-1)} [o(x)o] (1/(2a))·(-x)

int[ sin(x)·e^{x} ] d[x] = (-x) [o(x)o] cos(x) [o(x)o] e^{x} = ...

... (1/2)·( sin(x)·e^{x}+(-1)·cos(x)·e^{x} )

sin(x)·e^{x} = (1/2)·( ( cos(x)·e^{x}+sin(x)·e^{x} )+( sin(x)·e^{x}+(-1)·cos(x)·e^{x} ) )

int[ cos(x)·e^{x} ] d[x] = x [o(x)o] sin(x) [o(x)o] e^{x} = ...

... (1/2)·( sin(x)·e^{x}+cos(x)·e^{x} )

cos(x)·e^{x} = (1/2)·( ( cos(x)·e^{x}+sin(x)·e^{x} )+( (-1)·sin(x)·e^{x}+cos(x)·e^{x} ) )

int[ x^{p}·sin(x) ] d[x] = (-x) [o(x)o] (1/(p+1))·x^{p+1} [o(x)o] cos(x) = ...

... x^{p+1}·[sn-er]_{(2k+1)!:p+1}(x)

[sn-er]_{(2k+1)!:q}(x) = sum[ (-1)^{k}·( 1/(2k+1)! )·( 1/((2k+1)+q) )·x^{2k+1} ]

int[ x^{p}·cos(x) ] d[x] = x [o(x)o] (1/(p+1))·x^{p+1} [o(x)o] sin(x) = ...

... x^{p+1}·[sn-er]_{(2k)!:p+1}(x)

[sn-er]_{(2k)!:q}(x) = sum[ (-1)^{k}·( 1/(2k)! )·( 1/((2k)+q) )·x^{2k} ]