Integrales realizadas

89)CSC6x dx
=-16-1csc6-2x cotx+6-26-1csc6-2x dx
=15csc4xcotx+ 45csc4x dx
=csc⁴x5cotx+45-14-1csc4-2xcotx+4-24-1csc4-2x dx=csc⁴5xcotx+ 45-csc²3xcotx+23csc²x dx
=csc⁴5xcotx+ 45-csc²3xcotx+23-cotx+c
=csc⁴5xcotx-415csc²xcotx-23cotx+c
90)tg6x sec4x dx
=tg6x sec²x sec²xdx
=tg6x sec2x1+tg2xdx
=tg6x sec² x dx+tg8x sec² x dx
=tg⁷x7+tg⁹9+c
91) tg5x sec4x dx
=tg5sec2 x sec²x dx
=tg5x sec²x 1+tg2xdx=tg5x sec²x+tg6x sec²x dx
= tg⁶x6+tg⁸8+c
92)sen 5xcos2xdx
=12[13sen 3x 3dx+17sen 7x 7dx]
U=3x U= 7x
du=3dx du=7dx=-16cos3x-14cos7x+c
93)cos3xcos2xdx
m=3 n=2
sen mx sen nx = 12[cos3-2x-cos3+2x]
=12[cos1x dx-15cos5x dx
=12sen x-110sen5 ͯ+c94)cos3xcosxdx
m=3 n=1
=12cos3-1+cos4x
=12[12cos2x 2dx+14cos4x dx ]
=14 sen 2x+18 sen 4x+c
95) dxx²-4
Paso:2
(X²-4)=(x-2)(x+2)
Paso: 3
dxx²-2=[A(x-2)+B(x+2]dx
Paso: 4
= 1x²-4=Ax-2+Bx+2
=Ax-2+Bx+2=Ax+2+B(x-2)x-2(x+2)=Ax+2A+Bx-2Bx-2(x+2)
Paso: 51=Ax+Bx+2A-2B
1=2A-2B
0=Ax+Bx… 0=X(A+B)
0x=A+B
0=A+B
PASO:6
1=2A-2B
0=A+B
1=2A -2B
0=(A+B)²
1=2A-2B
0=2A+2B
1=4ª
A=14B=-14
96)x dx(x-2)²
x dx(x-2)²=[A(x-2)+B(x-2)²] dx
x(x-2)²=A(x-2)+B(x-2)²
xx-22=Ax-2+B(x-2)²=Ax-2A+B(x-2)2
X=Ax-2A+B
X=AX0=-2A+B
XX=A 0= (-2)(1)+B
A=1 B=2
1(X-2)dx+2(x-2)² dx
= lnx-2+2x-22dx
= lnx-2+2x-22+1+c
=lnx-2-2(x-2)+c