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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x^(1/2)
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Integral of x^1/2
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Integral of x*e^(2*x)
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Integral of arcsinx
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Identical expressions
- one /((one +5x)*(sixteen +x))
- 1 divide by ((1 plus 5x) multiply by (16 plus x))
- one divide by ((one plus 5x) multiply by (sixteen plus x))
- 1/((1+5x)(16+x))
- 1/1+5x16+x
- 1 divide by ((1+5x)*(16+x))
- 1/((1+5x)*(16+x))dx
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Similar expressions
- 1/((1-5x)*(16+x))
- 1/((1+5x)*(16-x))
Integral of 1/((1+5x)*(16+x)) dx
The solution
You have entered
[src]
1 / | | 1 | ------------------ dx | (1 + 5*x)*(16 + x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x + 16\right) \left(5 x + 1\right)}\, dx$$
Integral(1/((1 + 5*x)*(16 + x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ | | 1 log(16 + x) log(1 + 5*x) | ------------------ dx = C - ----------- + ------------ | (1 + 5*x)*(16 + x) 79 79 | /
$$\int \frac{1}{\left(x + 16\right) \left(5 x + 1\right)}\, dx = C - \frac{\log{\left(x + 16 \right)}}{79} + \frac{\log{\left(5 x + 1 \right)}}{79}$$
The graph
The answer
[src]
log(17) log(5) log(16) log(6/5)
- ------- + ------ + ------- + --------
79 79 79 79
$$- \frac{\log{\left(17 \right)}}{79} + \frac{\log{\left(\frac{6}{5} \right)}}{79} + \frac{\log{\left(5 \right)}}{79} + \frac{\log{\left(16 \right)}}{79}$$
=
=
log(17) log(5) log(16) log(6/5)
- ------- + ------ + ------- + --------
79 79 79 79
$$- \frac{\log{\left(17 \right)}}{79} + \frac{\log{\left(\frac{6}{5} \right)}}{79} + \frac{\log{\left(5 \right)}}{79} + \frac{\log{\left(16 \right)}}{79}$$
-log(17)/79 + log(5)/79 + log(16)/79 + log(6/5)/79
Use the examples entering the upper and lower limits of integration.