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How to use it?
- Integral of d{x}:
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Integral of e^((-x^2)/2)
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Integral of e^(x+2)
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Integral of xarctanx
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Integral of sin(2*x)
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Identical expressions
- ((three + two *tan(x))/(two *sin(x)^ two + three *cos(x)^ two)- one)
- ((3 plus 2 multiply by tangent of (x)) divide by (2 multiply by sinus of (x) squared plus 3 multiply by co sinus of e of (x) squared ) minus 1)
- ((three plus two multiply by tangent of (x)) divide by (two multiply by sinus of (x) to the power of two plus three multiply by co sinus of e of (x) to the power of two) minus one)
- ((3+2*tan(x))/(2*sin(x)2+3*cos(x)2)-1)
- 3+2*tanx/2*sinx2+3*cosx2-1
- ((3+2*tan(x))/(2*sin(x)²+3*cos(x)²)-1)
- ((3+2*tan(x))/(2*sin(x) to the power of 2+3*cos(x) to the power of 2)-1)
- ((3+2tan(x))/(2sin(x)^2+3cos(x)^2)-1)
- ((3+2tan(x))/(2sin(x)2+3cos(x)2)-1)
- 3+2tanx/2sinx2+3cosx2-1
- 3+2tanx/2sinx^2+3cosx^2-1
- ((3+2*tan(x)) divide by (2*sin(x)^2+3*cos(x)^2)-1)
- ((3+2*tan(x))/(2*sin(x)^2+3*cos(x)^2)-1)dx
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Similar expressions
- ((3+2*tan(x))/(2*sin(x)^2+3*cos(x)^2)+1)
- ((3+2*tan(x))/(2*sin(x)^2-3*cos(x)^2)-1)
- ((3-2*tan(x))/(2*sin(x)^2+3*cos(x)^2)-1)
- ((3+2*tan(x))/(2*sinx^2+3*cosx^2)-1)
Integral of ((3+2*tan(x))/(2*sin(x)^2+3*cos(x)^2)-1) dx
The solution
You have entered
[src]
/ ____\
|\/ 17 |
acos|------|
\ 17 /
/
|
| / 3 + 2*tan(x) \
| |--------------------- - 1| dx
| | 2 2 |
| \2*sin (x) + 3*cos (x) /
|
/
0
$$\int\limits_{0}^{\operatorname{acos}{\left(\frac{\sqrt{17}}{17} \right)}} \left(\left(-1\right) 1 + \frac{2 \tan{\left(x \right)} + 3}{2 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}\right)\, dx$$
Integral((3 + 2*tan(x))/(2*sin(x)^2 + 3*cos(x)^2) - 1*1, (x, 0, acos(sqrt(17)/17)))
Detail solution
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Integrate term-by-term:
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The integral of a constant is the constant times the variable of integration:
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Rewrite the integrand:
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Integrate term-by-term:
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The integral of a constant times a function is the constant times the integral of the function:
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Don't know the steps in finding this integral.
But the integral is
So, the result is:
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The integral of a constant times a function is the constant times the integral of the function:
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Don't know the steps in finding this integral.
But the integral is
So, the result is:
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The result is:
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The result is:
Now simplify:
Add the constant of integration:
The answer is:
The answer (Indefinite)
[src]
/ / / | | | | / 3 + 2*tan(x) \ | tan(x) | 1 | |--------------------- - 1| dx = C - x + 2* | --------------------- dx + 3* | --------------------- dx | | 2 2 | | 2 2 | 2 2 | \2*sin (x) + 3*cos (x) / | 2*sin (x) + 3*cos (x) | 2*sin (x) + 3*cos (x) | | | / / /
$$\int \left(\left(-1\right) 1 + \frac{2 \tan{\left(x \right)} + 3}{2 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}\right)\, dx = C - x + 2 \int \frac{\tan{\left(x \right)}}{2 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}\, dx + 3 \int \frac{1}{2 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}\, dx$$
The answer
[src]
/ ____\ / ____\
/ ____\ / ____\ |\/ 17 | |\/ 17 |
|\/ 17 | |\/ 17 | acos|------| acos|------|
acos|------| acos|------| \ 17 / \ 17 /
\ 17 / \ 17 / / /
/ / | |
| | | 2 | 2
| -3 | -2*tan(x) | 2*sin (x) | 3*cos (x)
- | --------------------- dx - | --------------------- dx - | --------------------- dx - | --------------------- dx
| 2 2 | 2 2 | 2 2 | 2 2
| 2*sin (x) + 3*cos (x) | 2*sin (x) + 3*cos (x) | 2*sin (x) + 3*cos (x) | 2*sin (x) + 3*cos (x)
| | | |
/ / / /
0 0 0 0
$$- \int\limits_{0}^{\operatorname{acos}{\left(\frac{\sqrt{17}}{17} \right)}} \frac{3 \cos^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}\, dx - \int\limits_{0}^{\operatorname{acos}{\left(\frac{\sqrt{17}}{17} \right)}} \frac{2 \sin^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}\, dx - \int\limits_{0}^{\operatorname{acos}{\left(\frac{\sqrt{17}}{17} \right)}} \left(- \frac{2 \tan{\left(x \right)}}{2 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}\right)\, dx - \int\limits_{0}^{\operatorname{acos}{\left(\frac{\sqrt{17}}{17} \right)}} \left(- \frac{3}{2 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}\right)\, dx$$
=
=
/ ____\ / ____\
/ ____\ / ____\ |\/ 17 | |\/ 17 |
|\/ 17 | |\/ 17 | acos|------| acos|------|
acos|------| acos|------| \ 17 / \ 17 /
\ 17 / \ 17 / / /
/ / | |
| | | 2 | 2
| -3 | -2*tan(x) | 2*sin (x) | 3*cos (x)
- | --------------------- dx - | --------------------- dx - | --------------------- dx - | --------------------- dx
| 2 2 | 2 2 | 2 2 | 2 2
| 2*sin (x) + 3*cos (x) | 2*sin (x) + 3*cos (x) | 2*sin (x) + 3*cos (x) | 2*sin (x) + 3*cos (x)
| | | |
/ / / /
0 0 0 0
$$- \int\limits_{0}^{\operatorname{acos}{\left(\frac{\sqrt{17}}{17} \right)}} \frac{3 \cos^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}\, dx - \int\limits_{0}^{\operatorname{acos}{\left(\frac{\sqrt{17}}{17} \right)}} \frac{2 \sin^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}\, dx - \int\limits_{0}^{\operatorname{acos}{\left(\frac{\sqrt{17}}{17} \right)}} \left(- \frac{2 \tan{\left(x \right)}}{2 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}\right)\, dx - \int\limits_{0}^{\operatorname{acos}{\left(\frac{\sqrt{17}}{17} \right)}} \left(- \frac{3}{2 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}\right)\, dx$$
Use the examples entering the upper and lower limits of integration.