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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of sinh^4x
- Integral of (e^(3x))*sin(x)
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Integral of cos(4x-5)dx
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Integral of (3x^2-4x+5)dx
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Identical expressions
- sinh^4x
- hyperbolic sinus of e of to the power of 4x
- sinh4x
- sinh⁴x
- sinh^4xdx
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Similar expressions
- sinh^4(x)
Integral of sinh^4x dx
The solution
You have entered
[src]
1 / | | 4 | sinh (x) dx | / 0
$$\int\limits_{0}^{1} \sinh^{4}{\left(x \right)}\, dx$$
Integral(sinh(x)^4, (x, 0, 1))
The answer (Indefinite)
[src]
/ | 3 4 4 3 2 2 | 4 3*cosh (x)*sinh(x) 3*x*cosh (x) 3*x*sinh (x) 5*sinh (x)*cosh(x) 3*x*cosh (x)*sinh (x) | sinh (x) dx = C - ------------------ + ------------ + ------------ + ------------------ - --------------------- | 8 8 8 8 4 /
$${{{{e^{4\,x}}\over{4}}-2\,e^{2\,x}+2\,e^ {- 2\,x }-{{e^ {- 4\,x }
}\over{4}}+6\,x}\over{16}}$$
The graph
The answer
[src]
4 4 2 2 3 3
3*cosh (1) 3*sinh (1) 3*cosh (1)*sinh (1) 3*cosh (1)*sinh(1) 5*sinh (1)*cosh(1)
---------- + ---------- - ------------------- - ------------------ + ------------------
8 8 4 8 8
$${{e^ {- 4 }\,\left(e^8-8\,e^6+24\,e^4+8\,e^2-1\right)}\over{64}}$$
=
=
4 4 2 2 3 3
3*cosh (1) 3*sinh (1) 3*cosh (1)*sinh (1) 3*cosh (1)*sinh(1) 5*sinh (1)*cosh(1)
---------- + ---------- - ------------------- - ------------------ + ------------------
8 8 4 8 8
$$- \frac{3 \sinh^{2}{\left(1 \right)} \cosh^{2}{\left(1 \right)}}{4} - \frac{3 \sinh{\left(1 \right)} \cosh^{3}{\left(1 \right)}}{8} + \frac{3 \sinh^{4}{\left(1 \right)}}{8} + \frac{5 \sinh^{3}{\left(1 \right)} \cosh{\left(1 \right)}}{8} + \frac{3 \cosh^{4}{\left(1 \right)}}{8}$$
The graph
Use the examples entering the upper and lower limits of integration.