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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*exp(x^3)
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Integral of 1/(2x-1)
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Integral of x(x^2+1)^3
- Integral of e^(1/x)
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Identical expressions
- (x*arctg)sqrt2x- one
- (x multiply by arctg) square root of 2x minus 1
- (x multiply by arctg) square root of 2x minus one
- (x*arctg)√2x-1
- (xarctg)sqrt2x-1
- xarctgsqrt2x-1
- (x*arctg)sqrt2x-1dx
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Similar expressions
- (x*arctg)sqrt2x+1
Integral of (x*arctg)sqrt2x-1 dx
The solution
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0 / | | / _____ \ | \x*atan(x)*\/ 2*x - 1/ dx | / 0
$$\int\limits_{0}^{0} \left(\sqrt{2 x} x \operatorname{atan}{\left(x \right)} - 1\right)\, dx$$
Integral((x*atan(x))*sqrt(2*x) - 1, (x, 0, 0))
The answer (Indefinite)
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/ | / ___ ___\ / ___ ___\ / ___ ___\ / ___ ___\ ___ 3/2 ___ 5/2 | / _____ \ log\2 + 2*x + 2*\/ 2 *\/ x / log\2 + 2*x - 2*\/ 2 *\/ x / 2*atan\1 + \/ 2 *\/ x / 2*atan\-1 + \/ 2 *\/ x / 4*\/ 2 *x 2*\/ 2 *x *atan(x) | \x*atan(x)*\/ 2*x - 1/ dx = C - x - ---------------------------- + ---------------------------- + ----------------------- + ------------------------ - ------------ + -------------------- | 5 5 5 5 15 5 /
$$\int \left(\sqrt{2 x} x \operatorname{atan}{\left(x \right)} - 1\right)\, dx = C + \frac{2 \sqrt{2} x^{\frac{5}{2}} \operatorname{atan}{\left(x \right)}}{5} - \frac{4 \sqrt{2} x^{\frac{3}{2}}}{15} - x + \frac{\log{\left(- 2 \sqrt{2} \sqrt{x} + 2 x + 2 \right)}}{5} - \frac{\log{\left(2 \sqrt{2} \sqrt{x} + 2 x + 2 \right)}}{5} + \frac{2 \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{5} + \frac{2 \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{5}$$
Use the examples entering the upper and lower limits of integration.