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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Compound Angles
∫tan23x+5 dx ...
Question
∫
tan
2
(
3
x
+
5
)
d
x
is equal to (where
C
is the constant of integration)
A
1
3
x
+
5
tan
(
3
x
+
5
)
−
x
+
C
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B
1
3
tan
(
3
x
+
5
)
+
x
+
C
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C
1
3
tan
(
3
x
+
5
)
−
x
+
C
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D
1
3
x
+
5
tan
(
3
x
+
5
)
+
x
+
C
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Solution
The correct option is
C
1
3
tan
(
3
x
+
5
)
−
x
+
C
I
=
∫
tan
2
(
3
x
+
5
)
d
x
=
∫
(
sec
2
(
3
x
+
5
)
−
1
)
d
x
=
∫
sec
2
(
3
x
+
5
)
d
x
−
∫
d
x
{
∵
∫
sec
2
(
a
x
+
b
)
d
x
=
1
a
tan
(
a
x
+
b
)
+
C
,
a
≠
0
}
=
1
3
tan
(
3
x
+
5
)
−
x
+
C
Suggest Corrections
2
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Standard XII Mathematics
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