Integrales

1)
dydx=3cos3x –3 sen 3x
(3cos3x -3 sen 3x) dx
=3 3 sen 3x+33cos3x +c v=3x
*y=sen 3x +cos 3x +c dv=3dx

x=π5 y=2.642

2.642= sen 3( π5 ) +cos3( π5 )+c
2.642=sen 336 +cos3 ( 36 ) +c
2.642=sen 108 +cos108 +c
2.642= 0.9510 -0.3090 +c
2.642=0.642 +c
2.642 -0.642=c
*2=c
*y=sen 3x +cos3x +2

2)
dydx=tanx2
y=- tanx2 dx v=x2
y= -2 tanx2 12dx
*y=2lncosx2 +c
x= π6 y=2
2=2lncosπ62 +c
2=2lncos302+ c
2=2lncos 15 +c
2=0.0693 +c
2 -0.0693=c
*2.0693=c
*y=2lncosπ2+ 2.0693

3)
dydx=33x +5
y= 33x+5 dx v=3x +5dv=3dx
*y=ln(3x+5)+c
x=5 y=-9
-9=ln35+5+c
-9=ln15+5+c
-9=ln20+c
-9=2.9957+c
-9-2.9957=c
*-12=c
*y=ln⁡(3x+5)-12

4)
dydx=20x4- 6x2+12x -10
y= 20x4 dx-6x2dx+12xdx +10dx
*y=4x5 -2x2+ 6x2-10x+c
x=2 y=128
128=20(2)55-6(2)33+12(2)22-10(2)+c
128=20325-683+1242- 20+c

128=128-16+24-20+c

128-116=c
*12=c
*y=4x5-2x2+6x2-10x+c

5)
dydx=e5x
y=e5x dxv=5x dv=5dx
*y=15e5x+ c
x=12 y=3.436

3.436=15 e5(12)+ c
3.436=15e52+ c
3.436=1512.182 +c
3.436=2.436 +c
3.436-2.436=c
*0.9996=c
*y=15e5x+ 0.9996

6)dydx=19x2-1
y=1dx9x2-1 v2=9x2 v=3x dv=3dx
y=133dx9x2-1
y=13 . 12(1)ln3x-13x+1+c
*y=16ln3x-13x+1+c
x=2 y=-4.115
-4.115=16ln3(2)-13(2)+1+c-4.115=16ln6-16+1+c
-4.115=16ln57+c
-4.115=0.0560+c
-4.115+0.0560=c
*-4.0596=c
*y=16ln3x-13x+1-4.0596

DERIVADA | FUNCION PRIMITIVA | VALORES DE LA FUNCION Y DE LA VARIABLE X | CONSTANTE DE LA INTEGRAL |FUNCION PRIMITIVA COMPLETA |
dydx=3cos3x -3 sen 3x | y=sen 3x+cos 3x+c | x=π5y=2.642 | 2 | y=sen 3x+cos 3x+2 |
dydx= -tanx2 | y= 2lncosx2+c | x=π6y=2 | 2.0693 | y=2lncosx2+2.0693 |dydx=33x+5 | y=ln3x+5+c | x=5y=-9 | -12 | y=ln3x+5-12 |
dydx= 20x4-6x2+12x-10 | y=4x5-2x3+6x2-10x+c | x=2y=128 | 12 | y=4x5-2x3+6x2-10x+12 |
dydx=e5x | y=15e5x+c | x=12y=3.436 | 0.9996 |...