Mister Exam
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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}:
- Integral of sqrt(e^x-9)
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Integral of 3x^4dx
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Integral of 1/sinx^2
- Integral of sin(2+3ln(x))/x
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Identical expressions
- sinxcosx÷(cos^ two x+3cosx+2)dx
- sinus of x co sinus of e of x÷( co sinus of e of squared x plus 3 co sinus of e of x plus 2)dx
- sinus of x co sinus of e of x÷( co sinus of e of to the power of two x plus 3 co sinus of e of x plus 2)dx
- sinxcosx÷(cos2x+3cosx+2)dx
- sinxcosx÷cos2x+3cosx+2dx
- sinxcosx÷(cos²x+3cosx+2)dx
- sinxcosx÷(cos to the power of 2x+3cosx+2)dx
- sinxcosx÷cos^2x+3cosx+2dx
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Similar expressions
- sinxcosx÷(cos^2x+3cosx-2)dx
- sinxcosx÷(cos^2x-3cosx+2)dx
Integral of sinxcosx÷(cos^2x+3cosx+2)dx dx
The solution
You have entered
[src]
POST_GRBEK_SMALL_pi
-------------------
2
/
|
| 1
| sin(x)*cos(x)*----------------------*1 dx
| 2
| cos (x) + 3*cos(x) + 2
|
/
0
$$\int\limits_{0}^{\frac{POST_{GRBEK SMALL \pi}}{2}} \sin{\left(x \right)} \cos{\left(x \right)} \frac{1}{\cos^{2}{\left(x \right)} + 3 \cos{\left(x \right)} + 2} \cdot 1\, dx$$
Integral(sin(x)*cos(x)*1/(cos(x)^2 + 3*cos(x) + 2), (x, 0, POST_GRBEK_SMALL_pi/2))
The answer (Indefinite)
[src]
/ | / 2 \ | 1 3*log(4 + 2*cos(x)) log\2 + cos (x) + 3*cos(x)/ 3*log(2 + 2*cos(x)) | sin(x)*cos(x)*----------------------*1 dx = C - ------------------- - --------------------------- + ------------------- | 2 2 2 2 | cos (x) + 3*cos(x) + 2 | /
$$\int \sin{\left(x \right)} \cos{\left(x \right)} \frac{1}{\cos^{2}{\left(x \right)} + 3 \cos{\left(x \right)} + 2} \cdot 1\, dx = C + \frac{3 \log{\left(2 \cos{\left(x \right)} + 2 \right)}}{2} - \frac{3 \log{\left(2 \cos{\left(x \right)} + 4 \right)}}{2} - \frac{\log{\left(\cos^{2}{\left(x \right)} + 3 \cos{\left(x \right)} + 2 \right)}}{2}$$
The answer
[src]
/ /POST_GRBEK_SMALL_pi\\ / /POST_GRBEK_SMALL_pi\\
-log(2) - 2*log|2 + cos|-------------------|| + 2*log(3) + log|1 + cos|-------------------||
\ \ 2 // \ \ 2 //
$$\log{\left(\cos{\left(\frac{POST_{GRBEK SMALL \pi}}{2} \right)} + 1 \right)} - 2 \log{\left(\cos{\left(\frac{POST_{GRBEK SMALL \pi}}{2} \right)} + 2 \right)} - \log{\left(2 \right)} + 2 \log{\left(3 \right)}$$
=
=
/ /POST_GRBEK_SMALL_pi\\ / /POST_GRBEK_SMALL_pi\\
-log(2) - 2*log|2 + cos|-------------------|| + 2*log(3) + log|1 + cos|-------------------||
\ \ 2 // \ \ 2 //
$$\log{\left(\cos{\left(\frac{POST_{GRBEK SMALL \pi}}{2} \right)} + 1 \right)} - 2 \log{\left(\cos{\left(\frac{POST_{GRBEK SMALL \pi}}{2} \right)} + 2 \right)} - \log{\left(2 \right)} + 2 \log{\left(3 \right)}$$
Use the examples entering the upper and lower limits of integration.