Integral of sinx/cosx*cosx dx
The solution
Detail solution
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There are multiple ways to do this integral.
Method #1
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Let u=cos(x)1.
Then let du=cos2(x)sin(x)dx and substitute du:
∫u21du
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The integral of un is n+1un+1 when n=−1:
∫u21du=−u1
Now substitute u back in:
−cos(x)
Method #2
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Let u=cos(x).
Then let du=−sin(x)dx and substitute −du:
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The integral of a constant times a function is the constant times the integral of the function:
∫(−1)du=−∫1du
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The integral of a constant is the constant times the variable of integration:
∫1du=u
So, the result is: −u
Now substitute u back in:
−cos(x)
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Add the constant of integration:
−cos(x)+constant
The answer is:
−cos(x)+constant
The answer (Indefinite)
[src]
/
|
| sin(x)*cos(x)
| ------------- dx = C - cos(x)
| cos(x)
|
/
∫cos(x)sin(x)cos(x)dx=C−cos(x)
The graph
1−cos(1)
=
1−cos(1)
Use the examples entering the upper and lower limits of integration.