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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 sqrt(1+x^2)/x
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Integral of t^2
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Integral of (x-1)^1/2
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Identical expressions
- (two tanx)/(one -tanx^2)
- (2 tangent of x) divide by (1 minus tangent of x squared )
- (two tangent of x) divide by (one minus tangent of x squared )
- (2tanx)/(1-tanx2)
- 2tanx/1-tanx2
- (2tanx)/(1-tanx²)
- (2tanx)/(1-tanx to the power of 2)
- 2tanx/1-tanx^2
- (2tanx) divide by (1-tanx^2)
- (2tanx)/(1-tanx^2)dx
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Similar expressions
- (2tanx)/(1+tanx^2)
Integral of (2tanx)/(1-tanx^2) dx
The solution
You have entered
[src]
1 / | | 2*tan(x) | ----------- dx | 2 | 1 - tan (x) | / 0
$$\int\limits_{0}^{1} \frac{2 \tan{\left(x \right)}}{1 - \tan^{2}{\left(x \right)}}\, dx$$
Integral((2*tan(x))/(1 - tan(x)^2), (x, 0, 1))
The answer (Indefinite)
[src]
/ | // / 2 \ 4 \ | 2*tan(x) ||-acoth\tan (x)/ for tan (x) > 1| | ----------- dx = C - |< | | 2 || / 2 \ 4 | | 1 - tan (x) \\-atanh\tan (x)/ for tan (x) < 1/ | /
$$\int \frac{2 \tan{\left(x \right)}}{1 - \tan^{2}{\left(x \right)}}\, dx = C - \begin{cases} - \operatorname{acoth}{\left(\tan^{2}{\left(x \right)} \right)} & \text{for}\: \tan^{4}{\left(x \right)} > 1 \\- \operatorname{atanh}{\left(\tan^{2}{\left(x \right)} \right)} & \text{for}\: \tan^{4}{\left(x \right)} < 1 \end{cases}$$
The graph
Use the examples entering the upper and lower limits of integration.