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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+2x^2)/(x^2(1+x^2))
- Integral of (x^2-y^2)/(x^2+y^2)^2
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Integral of (x^2)^(1/3)
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Integral of (x-2)^2dx
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Identical expressions
- one /(2sh(x)+3ch(x))
- 1 divide by (2sh(x) plus 3ch(x))
- one divide by (2sh(x) plus 3ch(x))
- 1/2shx+3chx
- 1 divide by (2sh(x)+3ch(x))
- 1/(2sh(x)+3ch(x))dx
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Similar expressions
- 1/(2sh(x)-3ch(x))
Integral of 1/(2sh(x)+3ch(x)) dx
The solution
You have entered
[src]
1 / | | 1 | 1*--------------------- dx | 2*sinh(x) + 3*cosh(x) | / 0
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{2 \sinh{\left(x \right)} + 3 \cosh{\left(x \right)}}\, dx$$
Integral(1/(2*sinh(x) + 3*cosh(x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ ___ /x\\
| ___ 3*\/ 5 *tanh|-||
/ ___ |2*\/ 5 \2/|
| 2*\/ 5 *atan|------- + ---------------|
| 1 \ 5 5 /
| 1*--------------------- dx = C + ---------------------------------------
| 2*sinh(x) + 3*cosh(x) 5
|
/
$$\int 1 \cdot \frac{1}{2 \sinh{\left(x \right)} + 3 \cosh{\left(x \right)}}\, dx = C + \frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{3 \sqrt{5} \tanh{\left(\frac{x}{2} \right)}}{5} + \frac{2 \sqrt{5}}{5} \right)}}{5}$$
The graph
The answer
[src]
/ ___\ / ___ ___ \
___ |2*\/ 5 | ___ |2*\/ 5 3*\/ 5 *tanh(1/2)|
2*\/ 5 *atan|-------| 2*\/ 5 *atan|------- + -----------------|
\ 5 / \ 5 5 /
- --------------------- + -----------------------------------------
5 5
$$- \frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}}{5} + \frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{3 \sqrt{5} \tanh{\left(\frac{1}{2} \right)}}{5} + \frac{2 \sqrt{5}}{5} \right)}}{5}$$
=
=
/ ___\ / ___ ___ \
___ |2*\/ 5 | ___ |2*\/ 5 3*\/ 5 *tanh(1/2)|
2*\/ 5 *atan|-------| 2*\/ 5 *atan|------- + -----------------|
\ 5 / \ 5 5 /
- --------------------- + -----------------------------------------
5 5
$$- \frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}}{5} + \frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{3 \sqrt{5} \tanh{\left(\frac{1}{2} \right)}}{5} + \frac{2 \sqrt{5}}{5} \right)}}{5}$$
The graph
Use the examples entering the upper and lower limits of integration.