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- Improper 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 x/(x^2+3)
- Integral of xcoscos(3x²+2)dx
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Integral of e^(-x)*x
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Identical expressions
- (x- one)/((2x+ one)(2x- three))
- (x minus 1) divide by ((2x plus 1)(2x minus 3))
- (x minus one) divide by ((2x plus one)(2x minus three))
- x-1/2x+12x-3
- (x-1) divide by ((2x+1)(2x-3))
- (x-1)/((2x+1)(2x-3))dx
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Similar expressions
- (x-1)/((2x-1)(2x-3))
- (x+1)/((2x+1)(2x-3))
- (x-1)/((2x+1)(2x+3))
Integral of (x-1)/((2x+1)(2x-3)) dx
The solution
You have entered
[src]
1 / | | x - 1 | ------------------- dx | (2*x + 1)*(2*x - 3) | / 0
$$\int\limits_{0}^{1} \frac{x - 1}{\left(2 x - 3\right) \left(2 x + 1\right)}\, dx$$
Integral((x - 1)/(((2*x + 1)*(2*x - 3))), (x, 0, 1))
The answer (Indefinite)
[src]
/ | | x - 1 log(-3 + 2*x) 3*log(1 + 2*x) | ------------------- dx = C + ------------- + -------------- | (2*x + 1)*(2*x - 3) 16 16 | /
$$\int \frac{x - 1}{\left(2 x - 3\right) \left(2 x + 1\right)}\, dx = C + \frac{\log{\left(2 x - 3 \right)}}{16} + \frac{3 \log{\left(2 x + 1 \right)}}{16}$$
The graph
The answer
[src]
log(2) log(3/2) ------ + -------- 8 8
$$\frac{\log{\left(\frac{3}{2} \right)}}{8} + \frac{\log{\left(2 \right)}}{8}$$
=
=
log(2) log(3/2) ------ + -------- 8 8
$$\frac{\log{\left(\frac{3}{2} \right)}}{8} + \frac{\log{\left(2 \right)}}{8}$$
log(2)/8 + log(3/2)/8
The graph
Use the examples entering the upper and lower limits of integration.