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How to use it?
- Integral of d{x}:
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Integral of x^-2
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Integral of (x+1)^2
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Integral of ln^2(x)
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Integral of ln(x)
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Identical expressions
- one /(x²+ two x+2)
- 1 divide by (x² plus 2x plus 2)
- one divide by (x² plus two x plus 2)
- 1/x²+2x+2
- 1 divide by (x²+2x+2)
- 1/(x²+2x+2)dx
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Similar expressions
- 1/(x²+2x-2)
- 1/(x²-2x+2)
Integral of 1/(x²+2x+2) dx
The solution
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[src]
1 / | | 1 | ------------ dx | 2 | x + 2*x + 2 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} + 2 x\right) + 2}\, dx$$
Integral(1/(x^2 + 2*x + 2), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | ------------ dx | 2 | x + 2*x + 2 | /
Rewrite the integrand
1 1 ------------ = ----------------- 2 / 2 \ x + 2*x + 2 1*\(-x - 1) + 1/
or
/ | | 1 | ------------ dx | 2 = | x + 2*x + 2 | /
/ | | 1 | ------------- dx | 2 | (-x - 1) + 1 | /
In the integral
/ | | 1 | ------------- dx | 2 | (-x - 1) + 1 | /
do replacement
v = -1 - x
then
the integral =
/ | | 1 | ------ dv = atan(v) | 2 | 1 + v | /
do backward replacement
/ | | 1 | ------------- dx = atan(1 + x) | 2 | (-x - 1) + 1 | /
Solution is:
C + atan(1 + x)
The answer (Indefinite)
[src]
/ | | 1 | ------------ dx = C + atan(1 + x) | 2 | x + 2*x + 2 | /
$$\int \frac{1}{\left(x^{2} + 2 x\right) + 2}\, dx = C + \operatorname{atan}{\left(x + 1 \right)}$$
The graph
The answer
[src]
pi - -- + atan(2) 4
$$- \frac{\pi}{4} + \operatorname{atan}{\left(2 \right)}$$
=
=
pi - -- + atan(2) 4
$$- \frac{\pi}{4} + \operatorname{atan}{\left(2 \right)}$$
-pi/4 + atan(2)
The graph
Use the examples entering the upper and lower limits of integration.