∫ sin 3 x cos 5 x 1 d x
The integral above is equals to a tan b x + c tan d x + constant . Where a , b , c , d are reals . Find the value of 3 ( a + b + c + d ) .
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The integral can be written as:
I
=
∫
tan
3
x
cos
8
x
sec
2
x
d
x
Now let
tan
x
=
t
, the integral becomes:
I
=
t
3
(
1
+
t
2
)
d
t
=
−
2
tan
2
1
x
+
3
2
tan
3
2
x
+
c
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