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Byju's Answer
Standard XII
Mathematics
Integration by Substitution
Evaluate: ∫...
Question
Evaluate:
∫
x
sec
2
x
d
x
Open in App
Solution
I
=
∫
x
sec
2
x
d
x
We know that
∫
u
v
=
u
∫
v
−
∫
(
∫
v
)
d
u
d
x
.
d
x
u
=
x
v
=
sec
2
x
I
=
x
∫
sec
2
x
−
∫
(
∫
sec
2
x
)
.1
d
x
I
=
x
tan
x
−
∫
tan
x
d
x
I
=
x
tan
x
−
ln
|
sec
x
|
+
c
.
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