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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*2^(-x)
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Integral of y^(-2/3)
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Integral of (x^2+1)/((x^3+3x+1)^5)
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Integral of sqrt(x^2-9)/x
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Identical expressions
- (8x-atan(two x))/(one +4x^2)
- (8x minus arc tangent of gent of (2x)) divide by (1 plus 4x squared )
- (8x minus arc tangent of gent of (two x)) divide by (one plus 4x squared )
- (8x-atan(2x))/(1+4x2)
- 8x-atan2x/1+4x2
- (8x-atan(2x))/(1+4x²)
- (8x-atan(2x))/(1+4x to the power of 2)
- 8x-atan2x/1+4x^2
- (8x-atan(2x)) divide by (1+4x^2)
- (8x-atan(2x))/(1+4x^2)dx
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Similar expressions
- (8x+atan(2x))/(1+4x^2)
- (8x-atan(2x))/(1-4x^2)
- (8x-arctan(2x))/(1+4x^2)
Integral of (8x-atan(2x))/(1+4x^2) dx
The solution
You have entered
[src]
1/2 / | | 8*x - atan(2*x) | --------------- dx | 2 | 1 + 4*x | / 0
$$\int\limits_{0}^{\frac{1}{2}} \frac{8 x - \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1}\, dx$$
Integral((8*x - atan(2*x))/(1 + 4*x^2), (x, 0, 1/2))
The answer (Indefinite)
[src]
/ | 2 | 8*x - atan(2*x) atan (2*x) / 2\ | --------------- dx = C - ---------- + log\2 + 8*x / | 2 4 | 1 + 4*x | /
$$\int \frac{8 x - \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1}\, dx = C + \log{\left(8 x^{2} + 2 \right)} - \frac{\operatorname{atan}^{2}{\left(2 x \right)}}{4}$$
The graph
Use the examples entering the upper and lower limits of integration.