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- Improper integral
- Double Integral
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How to use it?
- Integral of d{x}:
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Integral of y^(-2/3)
- Integral of x^(-x)
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Integral of x*sin(x)^2
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Integral of x^2/(1-x^4)
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Identical expressions
- (7x- one)/((x- three)^ two + four)
- (7x minus 1) divide by ((x minus 3) squared plus 4)
- (7x minus one) divide by ((x minus three) to the power of two plus four)
- (7x-1)/((x-3)2+4)
- 7x-1/x-32+4
- (7x-1)/((x-3)²+4)
- (7x-1)/((x-3) to the power of 2+4)
- 7x-1/x-3^2+4
- (7x-1) divide by ((x-3)^2+4)
- (7x-1)/((x-3)^2+4)dx
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Similar expressions
- (7x+1)/((x-3)^2+4)
- (7x-1)/((x+3)^2+4)
- (7x-1)/((x-3)^2-4)
Integral of (7x-1)/((x-3)^2+4) dx
The solution
You have entered
[src]
1 / | | 7*x - 1 | ------------ dx | 2 | (x - 3) + 4 | / 0
$$\int\limits_{0}^{1} \frac{7 x - 1}{\left(x - 3\right)^{2} + 4}\, dx$$
Integral((7*x - 1)/((x - 3)^2 + 4), (x, 0, 1))
The answer (Indefinite)
[src]
/ | / 2 \ | 7*x - 1 / 3 x\ 7*log\13 + x - 6*x/ | ------------ dx = C + 10*atan|- - + -| + -------------------- | 2 \ 2 2/ 2 | (x - 3) + 4 | /
$$\int \frac{7 x - 1}{\left(x - 3\right)^{2} + 4}\, dx = C + \frac{7 \log{\left(x^{2} - 6 x + 13 \right)}}{2} + 10 \operatorname{atan}{\left(\frac{x}{2} - \frac{3}{2} \right)}$$
The graph
The answer
[src]
7*log(13) 5*pi 7*log(8)
10*atan(3/2) - --------- - ---- + --------
2 2 2
$$- \frac{7 \log{\left(13 \right)}}{2} - \frac{5 \pi}{2} + \frac{7 \log{\left(8 \right)}}{2} + 10 \operatorname{atan}{\left(\frac{3}{2} \right)}$$
=
=
7*log(13) 5*pi 7*log(8)
10*atan(3/2) - --------- - ---- + --------
2 2 2
$$- \frac{7 \log{\left(13 \right)}}{2} - \frac{5 \pi}{2} + \frac{7 \log{\left(8 \right)}}{2} + 10 \operatorname{atan}{\left(\frac{3}{2} \right)}$$
10*atan(3/2) - 7*log(13)/2 - 5*pi/2 + 7*log(8)/2
Use the examples entering the upper and lower limits of integration.