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How to use it?
- Integral of d{x}:
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Integral of e^(-x)
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Integral of -sin(x)
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Integral of cos(x/2)
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Integral of x-2
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Identical expressions
- (x+ three)/(3x^ two +4x- one)
- (x plus 3) divide by (3x squared plus 4x minus 1)
- (x plus three) divide by (3x to the power of two plus 4x minus one)
- (x+3)/(3x2+4x-1)
- x+3/3x2+4x-1
- (x+3)/(3x²+4x-1)
- (x+3)/(3x to the power of 2+4x-1)
- x+3/3x^2+4x-1
- (x+3) divide by (3x^2+4x-1)
- (x+3)/(3x^2+4x-1)dx
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Similar expressions
- (x+3)/(3x^2+4x+1)
- (x+3)/(3x^2-4x-1)
- (x-3)/(3x^2+4x-1)
Integral of (x+3)/(3x^2+4x-1) dx
The solution
You have entered
[src]
1 / | | x + 3 | -------------- dx | 2 | 3*x + 4*x - 1 | / 0
$$\int\limits_{0}^{1} \frac{x + 3}{\left(3 x^{2} + 4 x\right) - 1}\, dx$$
Integral((x + 3)/(3*x^2 + 4*x - 1), (x, 0, 1))
The answer (Indefinite)
[src]
// / ___ \ \
|| ___ |3*\/ 7 *(2/3 + x)| |
||-\/ 7 *acoth|-----------------| |
/ || \ 7 / 2 |
| ||-------------------------------- for (2/3 + x) > 7/9| / 2 \
| x + 3 || 21 | log\-1 + 3*x + 4*x/
| -------------- dx = C + 7*|< | + --------------------
| 2 || / ___ \ | 6
| 3*x + 4*x - 1 || ___ |3*\/ 7 *(2/3 + x)| |
| ||-\/ 7 *atanh|-----------------| |
/ || \ 7 / 2 |
||-------------------------------- for (2/3 + x) < 7/9|
\\ 21 /
$$\int \frac{x + 3}{\left(3 x^{2} + 4 x\right) - 1}\, dx = C + 7 \left(\begin{cases} - \frac{\sqrt{7} \operatorname{acoth}{\left(\frac{3 \sqrt{7} \left(x + \frac{2}{3}\right)}{7} \right)}}{21} & \text{for}\: \left(x + \frac{2}{3}\right)^{2} > \frac{7}{9} \\- \frac{\sqrt{7} \operatorname{atanh}{\left(\frac{3 \sqrt{7} \left(x + \frac{2}{3}\right)}{7} \right)}}{21} & \text{for}\: \left(x + \frac{2}{3}\right)^{2} < \frac{7}{9} \end{cases}\right) + \frac{\log{\left(3 x^{2} + 4 x - 1 \right)}}{6}$$
The graph
Use the examples entering the upper and lower limits of integration.