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How to use it?
- Integral of d{x}:
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Integral of e^(2*x)*cos(3*x)
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Integral of (2x-4)
- Integral of (3-sin(x))/(2cos(x)+3tan(x))
- Integral of (x)/(x^3-1)
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Identical expressions
- (two x+ five)/(x^2+5x+ four)
- (2x plus 5) divide by (x squared plus 5x plus 4)
- (two x plus five) divide by (x squared plus 5x plus four)
- (2x+5)/(x2+5x+4)
- 2x+5/x2+5x+4
- (2x+5)/(x²+5x+4)
- (2x+5)/(x to the power of 2+5x+4)
- 2x+5/x^2+5x+4
- (2x+5) divide by (x^2+5x+4)
- (2x+5)/(x^2+5x+4)dx
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Similar expressions
- (2x+5)/(x^2+5x-4)
- (2x-5)/(x^2+5x+4)
- (2x+5)/(x^2-5x+4)
Integral of (2x+5)/(x^2+5x+4) dx
The solution
You have entered
[src]
1 / | | 2*x + 5 | ------------ dx | 2 | x + 5*x + 4 | / 0
$$\int\limits_{0}^{1} \frac{2 x + 5}{\left(x^{2} + 5 x\right) + 4}\, dx$$
Integral((2*x + 5)/(x^2 + 5*x + 4), (x, 0, 1))
Detail solution
We have the integral:
/ | | 2*x + 5 | ------------ dx | 2 | x + 5*x + 4 | /
Rewrite the integrand
True
or
/ | | 2*x + 5 | ------------ dx | 2 = | x + 5*x + 4 | /
/ | | 2*x + 5 | ------------ dx | 2 | x + 5*x + 4 | /
In the integral
/ | | 2*x + 5 | ------------ dx | 2 | x + 5*x + 4 | /
do replacement
2 u = x + 5*x
then
the integral =
/ | | 1 | ----- du = log(4 + u) | 4 + u | /
do backward replacement
/ | | 2*x + 5 / 2 \ | ------------ dx = log\4 + x + 5*x/ | 2 | x + 5*x + 4 | /
Solution is:
/ 2 \ C + log\4 + x + 5*x/
The answer (Indefinite)
[src]
/ | | 2*x + 5 / 2 \ | ------------ dx = C + log\x + 5*x + 4/ | 2 | x + 5*x + 4 | /
$$\int \frac{2 x + 5}{\left(x^{2} + 5 x\right) + 4}\, dx = C + \log{\left(\left(x^{2} + 5 x\right) + 4 \right)}$$
The graph
The answer
[src]
-log(4) + log(10)
$$- \log{\left(4 \right)} + \log{\left(10 \right)}$$
=
=
-log(4) + log(10)
$$- \log{\left(4 \right)} + \log{\left(10 \right)}$$
-log(4) + log(10)
The graph
Use the examples entering the upper and lower limits of integration.