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How to use it?
- Integral of d{x}:
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Integral of tanx^2
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Integral of tan((pi)(x)/2)
- Integral of sqrt(1+(1-sinx)^2)
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Integral of tan^2(4x)
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Identical expressions
- sech^ two (x)tanh^ five (x)
- sech squared (x) hyperbolic tangent of gent of to the power of 5(x)
- sech to the power of two (x) hyperbolic tangent of gent of to the power of five (x)
- sech2(x)tanh5(x)
- sech2xtanh5x
- sech²(x)tanh⁵(x)
- sech to the power of 2(x)tanh to the power of 5(x)
- sech^2xtanh^5x
- sech^2(x)tanh^5(x)dx
Integral of sech^2(x)tanh^5(x) dx
The solution
You have entered
[src]
3 / | | 2 5 | sech (x)*tanh (x) dx | / 2
$$\int\limits_{2}^{3} \tanh^{5}{\left(x \right)} \operatorname{sech}^{2}{\left(x \right)}\, dx$$
Integral(sech(x)^2*tanh(x)^5, (x, 2, 3))
The answer (Indefinite)
[src]
/ | 2 2 2 2 4 | 2 5 sech (x) sech (x)*tanh (x) sech (x)*tanh (x) | sech (x)*tanh (x) dx = C - -------- - ----------------- - ----------------- | 6 6 6 /
$${{\tanh ^6x}\over{6}}$$
The graph
The answer
[src]
2 2 2 2 2 4 2 2 2 4
sech (3) sech (2) sech (3)*tanh (3) sech (3)*tanh (3) sech (2)*tanh (2) sech (2)*tanh (2)
- -------- + -------- - ----------------- - ----------------- + ----------------- + -----------------
6 6 6 6 6 6
$${{6\,e^{20}+20\,e^{12}+6\,e^4}\over{3\,e^{24}+18\,e^{20}+45\,e^{16}
+60\,e^{12}+45\,e^8+18\,e^4+3}}-{{6\,e^{30}+20\,e^{18}+6\,e^6}\over{
3\,e^{36}+18\,e^{30}+45\,e^{24}+60\,e^{18}+45\,e^{12}+18\,e^6+3}}$$
=
=
2 2 2 2 2 4 2 2 2 4
sech (3) sech (2) sech (3)*tanh (3) sech (3)*tanh (3) sech (2)*tanh (2) sech (2)*tanh (2)
- -------- + -------- - ----------------- - ----------------- + ----------------- + -----------------
6 6 6 6 6 6
$$- \frac{\operatorname{sech}^{2}{\left(3 \right)}}{6} - \frac{\tanh^{2}{\left(3 \right)} \operatorname{sech}^{2}{\left(3 \right)}}{6} - \frac{\tanh^{4}{\left(3 \right)} \operatorname{sech}^{2}{\left(3 \right)}}{6} + \frac{\tanh^{4}{\left(2 \right)} \operatorname{sech}^{2}{\left(2 \right)}}{6} + \frac{\tanh^{2}{\left(2 \right)} \operatorname{sech}^{2}{\left(2 \right)}}{6} + \frac{\operatorname{sech}^{2}{\left(2 \right)}}{6}$$
The graph
Use the examples entering the upper and lower limits of integration.