slove the integration of sec30x tanx dx
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Step-by-step explanation:
When working with integrals of secant and tangent, it's important to remember the following:
d
d
x
tan
x
=
sec
2
x
d
d
x
sec
x
=
sec
x
tan
x
Here, we see that we can write
sec
3
x
(
tan
x
)
as
sec
2
x
(
sec
x
tan
x
)
, which is perfect, since it composed of
sec
2
x
and the derivative of secant,
sec
x
tan
x
. This indicates to us that we want to use a substitution of
u
=
sec
x
.
∫
sec
3
x
(
tan
x
)
d
x
=
∫
sec
2
x
(
sec
x
tan
x
)
d
x
With
u
=
sec
x
and
d
u
=
(
sec
x
tan
x
)
d
x
:
=
∫
u
2
d
u
=
u
3
3
+
C
=
sec
3
x
3
+
C
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