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- Improper integral
- Double Integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(x(1-x))
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Integral of x*sinh(x)
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Integral of x*2^(-x)*dx
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Integral of x^2+e^x
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Identical expressions
- one /(x^ two + six *x+ four)
- 1 divide by (x squared plus 6 multiply by x plus 4)
- one divide by (x to the power of two plus six multiply by x plus four)
- 1/(x2+6*x+4)
- 1/x2+6*x+4
- 1/(x²+6*x+4)
- 1/(x to the power of 2+6*x+4)
- 1/(x^2+6x+4)
- 1/(x2+6x+4)
- 1/x2+6x+4
- 1/x^2+6x+4
- 1 divide by (x^2+6*x+4)
- 1/(x^2+6*x+4)dx
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Similar expressions
- 1/(x^2-6*x+4)
- 1/(x^2+6*x-4)
Integral of 1/(x^2+6*x+4) dx
The solution
You have entered
[src]
1 / | | 1 | ------------ dx | 2 | x + 6*x + 4 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} + 6 x\right) + 4}\, dx$$
Integral(1/(x^2 + 6*x + 4), (x, 0, 1))
The answer (Indefinite)
[src]
// / ___ \ \
|| ___ |\/ 5 *(3 + x)| |
||-\/ 5 *acoth|-------------| |
/ || \ 5 / 2 |
| ||---------------------------- for (3 + x) > 5|
| 1 || 5 |
| ------------ dx = C + |< |
| 2 || / ___ \ |
| x + 6*x + 4 || ___ |\/ 5 *(3 + x)| |
| ||-\/ 5 *atanh|-------------| |
/ || \ 5 / 2 |
||---------------------------- for (3 + x) < 5|
\\ 5 /
$$\int \frac{1}{\left(x^{2} + 6 x\right) + 4}\, dx = C + \begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{\sqrt{5} \left(x + 3\right)}{5} \right)}}{5} & \text{for}\: \left(x + 3\right)^{2} > 5 \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{5} \left(x + 3\right)}{5} \right)}}{5} & \text{for}\: \left(x + 3\right)^{2} < 5 \end{cases}$$
The graph
The answer
[src]
___ / ___\ ___ / ___\ ___ / ___\ ___ / ___\
\/ 5 *log\3 - \/ 5 / \/ 5 *log\4 + \/ 5 / \/ 5 *log\3 + \/ 5 / \/ 5 *log\4 - \/ 5 /
- -------------------- - -------------------- + -------------------- + --------------------
10 10 10 10
$$- \frac{\sqrt{5} \log{\left(\sqrt{5} + 4 \right)}}{10} - \frac{\sqrt{5} \log{\left(3 - \sqrt{5} \right)}}{10} + \frac{\sqrt{5} \log{\left(4 - \sqrt{5} \right)}}{10} + \frac{\sqrt{5} \log{\left(\sqrt{5} + 3 \right)}}{10}$$
=
=
___ / ___\ ___ / ___\ ___ / ___\ ___ / ___\
\/ 5 *log\3 - \/ 5 / \/ 5 *log\4 + \/ 5 / \/ 5 *log\3 + \/ 5 / \/ 5 *log\4 - \/ 5 /
- -------------------- - -------------------- + -------------------- + --------------------
10 10 10 10
$$- \frac{\sqrt{5} \log{\left(\sqrt{5} + 4 \right)}}{10} - \frac{\sqrt{5} \log{\left(3 - \sqrt{5} \right)}}{10} + \frac{\sqrt{5} \log{\left(4 - \sqrt{5} \right)}}{10} + \frac{\sqrt{5} \log{\left(\sqrt{5} + 3 \right)}}{10}$$
-sqrt(5)*log(3 - sqrt(5))/10 - sqrt(5)*log(4 + sqrt(5))/10 + sqrt(5)*log(3 + sqrt(5))/10 + sqrt(5)*log(4 - sqrt(5))/10
Use the examples entering the upper and lower limits of integration.