integration(cosx+sinx)^2dx
Answers
Answered by
2
Step-by-step explanation:
Explanation:
∫
(
sin
(
x
)
+
cos
(
x
)
)
2
d
x
=
∫
sin
2
(
x
)
+
cos
2
(
x
)
+
2
sin
(
x
)
cos
(
x
)
d
x
{Expanding}
=
∫
1
+
2
sin
(
x
)
cos
(
x
)
d
x
{Since
sin
2
(
x
)
+
cos
2
(
x
)
=
1
}
=
∫
1
d
x
+
2
∫
sin
(
x
)
cos
(
x
)
d
x
{Linearity of integration}
=
x
+
C
+
2
∫
sin
(
x
)
cos
(
x
)
d
x
Now, substitue
u
=
sin
(
x
)
, or
d
x
=
d
u
cos
(
x
)
=
x
+
C
+
2
∫
u
cos
(
x
)
cos
(
x
)
d
u
=
x
+
C
+
2
∫
u
d
u
=
x
+
C
+
2
u
2
2
=
x
+
C
+
u
2
=
x
+
sin
2
(
x
)
+
C
Answered by
2
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