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a
x
u
a
x
u
Dari gambar diatas didapat
sinu = x x
u = sin
a
a
a sinu = x a cos u du = dx
adi x a dx = a cosu (a cos u du) = a cos u du
= a ( cos u) du = a (u sin u)
= a x
(sin
a
= a x
sin
a
sinu cosu) = a x
(sin
a
x a x (terbukti)
x
a
a
a
x
Bukti
a x dx = a ln x x a
x
a a x ( . )
x a x
Dari gambar diatas didapat
tanu = x x
u = tan
a
a
a tanu = x a sec du = dx
a
a x dx = a sec u du = a
cos u du = a cosu
cos u du
Misal v = sinu dv = cosu du
a x dx = a sec u du = a
cos u du = a cosu
cos u du
= a
d
( ) = a d d
( )
d d
( )
= a ln( ) ( ) ln( ) ( )
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