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- Improper integral
- Double Integral
- Triple Integral
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How to use it?
- Integral of d{x}:
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Integral of sin(5x)
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Integral of e^x/sqrt(e^(2*x)-1)
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Integral of e^(-x)/sqrt(x)
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Integral of cos(3x)dx
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Identical expressions
- ln((exp(one /x)+ six)/ five)
- ln(( exponent of (1 divide by x) plus 6) divide by 5)
- ln(( exponent of (one divide by x) plus six) divide by five)
- lnexp1/x+6/5
- ln((exp(1 divide by x)+6) divide by 5)
- ln((exp(1/x)+6)/5)dx
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Similar expressions
- ln((exp(1/x)-6)/5)
Integral of ln((exp(1/x)+6)/5) dx
The solution
You have entered
[src]
oo / | | / 1 \ | | - | | | x | | |e + 6| | log|------| dx | \ 5 / | / 1
$$\int\limits_{1}^{\infty} \log{\left(\frac{e^{\frac{1}{x}} + 6}{5} \right)}\, dx$$
Integral(log((exp(1/x) + 6)/5), (x, 1, oo))
The answer (Indefinite)
[src]
/ /
| |
| / 1 \ / 1 \ | 1
| | - | | - | | -
| | x | | x | | x
| |e + 6| |e + 6| | e
| log|------| dx = C + x*log|------| + | ---------- dx
| \ 5 / \ 5 / | / 1\
| | | -|
/ | | x|
| x*\6 + e /
|
/
$$\int \log{\left(\frac{e^{\frac{1}{x}} + 6}{5} \right)}\, dx = C + x \log{\left(\frac{e^{\frac{1}{x}} + 6}{5} \right)} + \int \frac{e^{\frac{1}{x}}}{x \left(e^{\frac{1}{x}} + 6\right)}\, dx$$
The answer
[src]
oo
/
|
| 1
| -
| x
| e
oo + | ---------- dx
| / 1\
| | -|
| | x|
| x*\6 + e /
|
/
1
$$\int\limits_{1}^{\infty} \frac{e^{\frac{1}{x}}}{x \left(e^{\frac{1}{x}} + 6\right)}\, dx + \infty$$
=
=
oo
/
|
| 1
| -
| x
| e
oo + | ---------- dx
| / 1\
| | -|
| | x|
| x*\6 + e /
|
/
1
$$\int\limits_{1}^{\infty} \frac{e^{\frac{1}{x}}}{x \left(e^{\frac{1}{x}} + 6\right)}\, dx + \infty$$
oo + Integral(exp(1/x)/(x*(6 + exp(1/x))), (x, 1, oo))
Use the examples entering the upper and lower limits of integration.