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- Improper integral
- Double Integral
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- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(2sinx+3cosx-5)
- Integral of a^(3logx)dx
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Integral of (7x-2)/(x^2-1)^(1/2)
- Integral of 1/(4cos(x)-3sinx)
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Identical expressions
- one /(2sinx+3cosx- five)
- 1 divide by (2 sinus of x plus 3 co sinus of e of x minus 5)
- one divide by (2 sinus of x plus 3 co sinus of e of x minus five)
- 1/2sinx+3cosx-5
- 1 divide by (2sinx+3cosx-5)
- 1/(2sinx+3cosx-5)dx
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Similar expressions
- 1/(2sinx+3cosx+5)
- 1/(2sinx-3cosx-5)
Integral of 1/(2sinx+3cosx-5) dx
The solution
You have entered
[src]
1 / | | 1 | 1*----------------------- dx | 2*sin(x) + 3*cos(x) - 5 | / 0
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{2 \sin{\left(x \right)} + 3 \cos{\left(x \right)} - 5}\, dx$$
Integral(1/(2*sin(x) + 3*cos(x) - 1*5), (x, 0, 1))
The answer (Indefinite)
[src]
/ /x pi\ / ___ /x\\\
| |- - --| | ___ 4*\/ 3 *tan|-|||
/ ___ | |2 2 | | \/ 3 \2/||
| \/ 3 *|pi*floor|------| + atan|- ----- + --------------||
| 1 \ \ pi / \ 3 3 //
| 1*----------------------- dx = C - ---------------------------------------------------------
| 2*sin(x) + 3*cos(x) - 5 3
|
/
$$-{{\arctan \left({{{{8\,\sin x}\over{\cos x+1}}-2}\over{2\,\sqrt{3}
}}\right)}\over{\sqrt{3}}}$$
The graph
The answer
[src]
/ / ___ ___ \\
___ | |\/ 3 4*\/ 3 *tan(1/2)||
___ \/ 3 *|-pi - atan|----- - ----------------||
7*pi*\/ 3 \ \ 3 3 //
- ---------- - --------------------------------------------
18 3
$$-{{\arctan \left({{4\,\sqrt{3}\,\sin 1-\sqrt{3}\,\cos 1-\sqrt{3}
}\over{3\,\cos 1+3}}\right)}\over{\sqrt{3}}}-{{\pi}\over{2\,3^{{{3
}\over{2}}}}}$$
=
=
/ / ___ ___ \\
___ | |\/ 3 4*\/ 3 *tan(1/2)||
___ \/ 3 *|-pi - atan|----- - ----------------||
7*pi*\/ 3 \ \ 3 3 //
- ---------- - --------------------------------------------
18 3
$$- \frac{7 \sqrt{3} \pi}{18} - \frac{\sqrt{3} \left(- \pi - \operatorname{atan}{\left(- \frac{4 \sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} + \frac{\sqrt{3}}{3} \right)}\right)}{3}$$
The graph
Use the examples entering the upper and lower limits of integration.