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How to use it?
- Integral of d{x}:
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Integral of -4*x*exp(-2*x)
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Integral of arcsin
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Integral of (x+2)e^x
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Integral of 1/(sqrt(1+x^2))
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Identical expressions
- abs(x^2arctan(2x))
- abs(x squared arc tangent of (2x))
- abs(x2arctan(2x))
- absx2arctan2x
- abs(x²arctan(2x))
- abs(x to the power of 2arctan(2x))
- absx^2arctan2x
- abs(x^2arctan(2x))dx
Integral of abs(x^2arctan(2x)) dx
The solution
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[src]
121 --- 100 / | | | 2 | | |x *atan(2*x)| dx | / -121 ----- 100
$$\int\limits_{- \frac{121}{100}}^{\frac{121}{100}} \left|{x^{2} \operatorname{atan}{\left(2 x \right)}}\right|\, dx$$
Integral(Abs(x^2*atan(2*x)), (x, -121/100, 121/100))
The answer
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121 --- 100 / | | / 3 | | x 2 x 2*x | |- - + x *atan(2*x) + ------------ + ------------ for atan(2*x) >= 0 | | 6 / 2\ / 2\ | | 6*\1 + 4*x / 3*\1 + 4*x / | < dx | | 3 | | x 2 2*x x | | - - x *atan(2*x) - ------------ - ------------ otherwise | | 6 / 2\ / 2\ | \ 3*\1 + 4*x / 6*\1 + 4*x / | / -121 ----- 100
$$\int_{-{{121}\over{100}}}^{{{121}\over{100}}}{{\it Abs}\left(x^2\,
\arctan \left(2\,x\right)\right)\;dx}$$
=
=
121 --- 100 / | | / 3 | | x 2 x 2*x | |- - + x *atan(2*x) + ------------ + ------------ for atan(2*x) >= 0 | | 6 / 2\ / 2\ | | 6*\1 + 4*x / 3*\1 + 4*x / | < dx | | 3 | | x 2 2*x x | | - - x *atan(2*x) - ------------ - ------------ otherwise | | 6 / 2\ / 2\ | \ 3*\1 + 4*x / 6*\1 + 4*x / | / -121 ----- 100
$$\int\limits_{- \frac{121}{100}}^{\frac{121}{100}} \begin{cases} \frac{2 x^{3}}{3 \cdot \left(4 x^{2} + 1\right)} + x^{2} \operatorname{atan}{\left(2 x \right)} - \frac{x}{6} + \frac{x}{6 \cdot \left(4 x^{2} + 1\right)} & \text{for}\: \operatorname{atan}{\left(2 x \right)} \geq 0 \\- \frac{2 x^{3}}{3 \cdot \left(4 x^{2} + 1\right)} - x^{2} \operatorname{atan}{\left(2 x \right)} + \frac{x}{6} - \frac{x}{6 \cdot \left(4 x^{2} + 1\right)} & \text{otherwise} \end{cases}\, dx$$
Use the examples entering the upper and lower limits of integration.