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- Integral of d{x}:
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Integral of 1/1+e^x
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Integral of tan^3(x)dx
- Integral of (-log(x))/x^2
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Integral of dx/(e^x-1)
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Identical expressions
- ln(two -x^ two)
- ln(2 minus x squared )
- ln(two minus x to the power of two)
- ln(2-x2)
- ln2-x2
- ln(2-x²)
- ln(2-x to the power of 2)
- ln2-x^2
- ln(2-x^2)dx
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Similar expressions
- ln(2+x^2)
Integral of ln(2-x^2) dx
The solution
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[src]
11 -- 10 / | | / 2\ | log\2 - x / dx | / 0
$$\int\limits_{0}^{\frac{11}{10}} \log{\left(2 - x^{2} \right)}\, dx$$
Integral(log(2 - x^2), (x, 0, 11/10))
The answer (Indefinite)
[src]
// / ___\ \
|| ___ |x*\/ 2 | |
||-\/ 2 *acoth|-------| |
/ || \ 2 / 2 |
| ||---------------------- for x > 2|
| / 2\ || 2 | / 2\
| log\2 - x / dx = C - 4*|< | - 2*x + x*log\2 - x /
| || / ___\ |
/ || ___ |x*\/ 2 | |
||-\/ 2 *atanh|-------| |
|| \ 2 / 2 |
||---------------------- for x < 2|
\\ 2 /
$$\int \log{\left(2 - x^{2} \right)}\, dx = C + x \log{\left(2 - x^{2} \right)} - 2 x - 4 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} & \text{for}\: x^{2} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} & \text{for}\: x^{2} < 2 \end{cases}\right)$$
The graph
The answer
[src]
/ 79\
11*log|---|
11 \100/ ___ / / ___\\ ___ /11 ___\ ___ / / 11 ___\\ ___ / ___\
- -- + ----------- + \/ 2 *\pi*I + log\\/ 2 // + \/ 2 *log|-- + \/ 2 | - \/ 2 *|pi*I + log|- -- + \/ 2 || - \/ 2 *log\\/ 2 /
5 10 \10 / \ \ 10 //
$$- \frac{11}{5} - \sqrt{2} \log{\left(\sqrt{2} \right)} + \frac{11 \log{\left(\frac{79}{100} \right)}}{10} + \sqrt{2} \log{\left(\frac{11}{10} + \sqrt{2} \right)} - \sqrt{2} \left(\log{\left(- \frac{11}{10} + \sqrt{2} \right)} + i \pi\right) + \sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right)$$
=
=
/ 79\
11*log|---|
11 \100/ ___ / / ___\\ ___ /11 ___\ ___ / / 11 ___\\ ___ / ___\
- -- + ----------- + \/ 2 *\pi*I + log\\/ 2 // + \/ 2 *log|-- + \/ 2 | - \/ 2 *|pi*I + log|- -- + \/ 2 || - \/ 2 *log\\/ 2 /
5 10 \10 / \ \ 10 //
$$- \frac{11}{5} - \sqrt{2} \log{\left(\sqrt{2} \right)} + \frac{11 \log{\left(\frac{79}{100} \right)}}{10} + \sqrt{2} \log{\left(\frac{11}{10} + \sqrt{2} \right)} - \sqrt{2} \left(\log{\left(- \frac{11}{10} + \sqrt{2} \right)} + i \pi\right) + \sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right)$$
-11/5 + 11*log(79/100)/10 + sqrt(2)*(pi*i + log(sqrt(2))) + sqrt(2)*log(11/10 + sqrt(2)) - sqrt(2)*(pi*i + log(-11/10 + sqrt(2))) - sqrt(2)*log(sqrt(2))
Use the examples entering the upper and lower limits of integration.