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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of x^2/sqrt(1+x^2)
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Integral of x/(x^2+2x+2)
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Integral of e^(x*(-4))
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Integral of sin^3x/cosx
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Identical expressions
- ((cos*x)*dx)/sqrt((2sin*x)+ one)
- (( co sinus of e of multiply by x) multiply by dx) divide by square root of ((2 sinus of multiply by x) plus 1)
- (( co sinus of e of multiply by x) multiply by dx) divide by square root of ((2 sinus of multiply by x) plus one)
- ((cos*x)*dx)/√((2sin*x)+1)
- ((cosx)dx)/sqrt((2sinx)+1)
- cosxdx/sqrt2sinx+1
- ((cos*x)*dx) divide by sqrt((2sin*x)+1)
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Similar expressions
- ((cos*x)*dx)/sqrt((2sin*x)-1)
- (cosxdx)/sqrt2sinx+1
Integral of ((cos*x)*dx)/sqrt((2sin*x)+1) dx
The solution
You have entered
[src]
p - 2 / | | cos(x) | ---------------- dx | ______________ | \/ 2*sin(x) + 1 | / 0
$$\int\limits_{0}^{\frac{p}{2}} \frac{\cos{\left(x \right)}}{\sqrt{2 \sin{\left(x \right)} + 1}}\, dx$$
Integral(cos(x)/sqrt(2*sin(x) + 1), (x, 0, p/2))
Detail solution
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Let .
Then let and substitute :
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The integral of a constant is the constant times the variable of integration:
Now substitute back in:
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Now simplify:
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Add the constant of integration:
The answer is:
The answer (Indefinite)
[src]
/ | | cos(x) ______________ | ---------------- dx = C + \/ 2*sin(x) + 1 | ______________ | \/ 2*sin(x) + 1 | /
$$\int \frac{\cos{\left(x \right)}}{\sqrt{2 \sin{\left(x \right)} + 1}}\, dx = C + \sqrt{2 \sin{\left(x \right)} + 1}$$
The answer
[src]
______________
/ /p\
-1 + / 1 + 2*sin|-|
\/ \2/
$$\sqrt{2 \sin{\left(\frac{p}{2} \right)} + 1} - 1$$
=
=
______________
/ /p\
-1 + / 1 + 2*sin|-|
\/ \2/
$$\sqrt{2 \sin{\left(\frac{p}{2} \right)} + 1} - 1$$
-1 + sqrt(1 + 2*sin(p/2))
Use the examples entering the upper and lower limits of integration.