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Byju's Answer
Standard XII
Mathematics
Integration by Substitution
Integrate the...
Question
Integrate the following function with respect to
x
1
sin
x
−
cos
x
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Solution
Marks
1
2
3
4
5
6
7
8
9
Frequency
1
2
1
3
5
4
2
1
1
∫
1
sin
x
−
cos
x
×
sin
x
+
cos
x
sin
x
+
cos
x
∫
sin
x
+
cos
x
sin
2
x
−
cos
2
x
∴
∫
sin
x
+
cos
x
2
sin
2
x
−
1
⇒
−
∫
sin
x
+
cos
x
1
−
2
sin
2
x
⇒
(
1
)
∫
sin
x
cos
2
x
d
x
=
1
2
√
2
(
ln
/
2
sin
x
+
√
2
−
ln
/
2
sin
x
−
√
2
)
⇒
1
2
√
2
ln
|
2
sin
x
+
√
2
|
−
ln
I
2
sin
x
−
√
2
I
Thus
∫
1
sin
x
−
cos
x
d
x
=
∫
cos
x
−
sin
x
cos
2
x
d
x
=
∫
−
sin
x
cos
3
x
+
∫
cos
x
cos
3
x
d
x
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