Integrales

1.

lnxdx u= lnx v= x
lnxx- ∫x1x dx du= 1x dx dv= dx
lnxx- ∫dxxlnx-x+c

2.
x ex dx u= x v= ex
exx- ∫ex dx du= dx dv= exdxxex- ex +c
ex(x-1)+c

3.
ln⁡(x)x2 dx u= lnx v= -1x
-lnx1x - -1x*1x dx du= 1x dxdv= x-2dx
-lnx1x + 1x2dx
-lnx1x -1x +c
-1x(lnx+1) +c

4.
x e5x dx u= x v= e5x5
e5x5x- ∫e5x5 dxdu= dx dv= e5xdx
xe5x5-15∫e5xdx
xe5x5- e5x25+c
e5x5(x-15)+c

5.
x2 ex dx u= x2v= ex
x2 ex- ∫ex 2x dx du= 2x dx dv= exdx
x2 ex-2∫ex x dx
x2 ex- 2 (ex(x-1))+c
x2 ex-2xex+2ex+c
ex(x2-2x+2)+c

6.ex cos⁡(2x) dx u= cos2x v= ex
cos⁡(2x) ex- ∫ex (-2sen(2x)) dx du= -2sen(2x) dx dv= exdxcos2xex+2∫ex sen(2x) dx
cos2xex+ 2 sen2xex-2 excos2xdx= ex cos⁡(2x) dx
cos2xex+ 2 sen2xex = 5 ex cos⁡(2x) dx
ex cos⁡(2x) dx= ex5cos2x + 2sen2x+c

7.
x cos⁡(x) dxu= x v= sen(x)
x sen(x) - ∫sen(x) dx du= dx dv= cos⁡(x)dx
x senx+ cosx+c
8.x2lnxdx u= lnx v= x33

lnxx33- ∫x33*1x dx du= 1x dx dv=...