Gabriel Marcel

(4x3 +3x2+2x) dx
4x4+3x3+2x24 3 2=
x4+x3+x2+c

(3x5+2x3+x-1) dx
3x6+2x4+x2-x 6 4 2 1=
x6+2x4+x2-x2 2 2 +c

dxx2
x-2dxx2+1-2+1 = x-1-1=-1x + c

x4 dx
x55

x dx
x22 + c

5 dx
5x + c



dxx5
x-5dx
x-4-4 = -4x4 + c

ʃ3x5dx
x53+153+1=x8/38/3=338x8+cxmdx

dx4x9x9+14-(-9+1)=x-84-(8)=x-8-32=132x8+c

ʃ (1x4-4x3+13x2+2x)dx
(1x-3-3-4x-2-2++x-13(-1)2x22)
(-12x3-42x2-13x+x2)+c
(-13x3+2x2-13x+x2)+c

ʃ(x5-1x4-2x6+x3)dx
=x57+157+1-=x-4+1-3--2-6+1-5+x5+14
=x127127+2x-55+x44=727x12+13x+-25x5+x44+1

ʃ dxx2
ʃx-2 dx
x-2+1-2+1=x-1-1=1x+c

(4x6-6x5+4x4-3x3+4x2+3x+10) dx
4x7- 6x6+4x5-3x4+4x3+3x2+10x7 6 5 4 3 2 14x7- x6+4x5-3x4+4x3+3x2+10x7 5 4 3 2 +c

ʃ dxx5
ʃx-5dx
x-4-4=-4x4+c

ʃ dx4x9=x-9+14-(-9+1)=x-84(-8)=x-8-32=132x8+c

ʃx5dx
ʃ x5/2dxx52+152+1=x7/27/2=27x7+c

ʃ dx3x11
3x-11+1-11+1=3x-10-10=3x-1010+c
310x10+c

ʃ (senx+cos⁡x)/cos⁡x dx
ʃ(senx/cos⁡x +cos⁡x/cos⁡x )dx
ʃ( tanx + 1 )dx
|n| secx|+x +c

° ʃ tan 2x dxd/dx(1/2 x)= 1/2(2)=1
2 ʃsen 1/2x dx
-2 cos 1/(2x ) +c

tan2x dx
ddx2x=212=1
12tan2x dx
12nsec2x|+c

x cotan x2 dx
ddx(x2)=2x12=x
12cotanx2 dx
12nsenx2|+c

secc22ax dx1ddx2ax=2a12a=1

12asec2|2ax|dx
12a+an 2ax+m

cos3x dx
ddx3x=3(13)=1
13cos3xdx
13sen3x+c


sen 12x dx
ddx12x=12*22=1
2sec12xdx
-2 cos12x+c

ʃ cos 3x dxd/dx(3x)=3(1/3)=1
1/3 ʃ cos 3x dx = 1/3 sen 3x +c

° ʃ senx/cos⁡〖2 x〗 dx
ʃ senx/cos⁡〖x .cosx〗 dx
ʃtan x secx dx
sec x + c


ʃ sec^2 2ª x dx
d/dx(2ax)=2ª (1/2a)=1
1/2a ʃsec^2|2ax|dx1/2a tan 2ax +m

° ʃ(x^2-2x)√(5&x) dx
ʃ(x^2-2x) x^(1/5)
ʃ(x^(15/5+1)/(16/5)-〖2x〗^(11/5)/(11/5)
5/6 √(5&x^16 )-10/11 √(5&x^11 )

ʃ e^(-x) dx
d/dx(-x)=-1(-1)=1...