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How to use it?
- Integral of d{x}:
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Integral of dx/(1+x^2)
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Integral of exp(y)
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Integral of -exp(-x)
- Integral of ln(x)/√x
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Identical expressions
- (one /sqrt(x))*arctg(x/ two +x)
- (1 divide by square root of (x)) multiply by arctg(x divide by 2 plus x)
- (one divide by square root of (x)) multiply by arctg(x divide by two plus x)
- (1/√(x))*arctg(x/2+x)
- (1/sqrt(x))arctg(x/2+x)
- 1/sqrtxarctgx/2+x
- (1 divide by sqrt(x))*arctg(x divide by 2+x)
- (1/sqrt(x))*arctg(x/2+x)dx
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Similar expressions
- (1/sqrt(x))*arctg(x/2-x)
Integral of (1/sqrt(x))*arctg(x/2+x) dx
The solution
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oo / | | /x \ | atan|- + x| | \2 / | ----------- dx | ___ | \/ x | / 2
$$\int\limits_{2}^{\infty} \frac{\operatorname{atan}{\left(\frac{x}{2} + x \right)}}{\sqrt{x}}\, dx$$
Integral(atan(x/2 + x)/sqrt(x), (x, 2, oo))
The answer (Indefinite)
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/ | / ___ ___\ / ___ ___\ | /x \ ___ |2 2*\/ 3 *\/ x | ___ |2 2*\/ 3 *\/ x | | atan|- + x| ___ / ___ ___\ ___ / ___ ___\ \/ 3 *log|- + x - -------------| \/ 3 *log|- + x + -------------| | \2 / ___ /x \ 2*\/ 3 *atan\1 + \/ 3 *\/ x / 2*\/ 3 *atan\-1 + \/ 3 *\/ x / \3 3 / \3 3 / | ----------- dx = C + 2*\/ x *atan|- + x| - ----------------------------- - ------------------------------ - -------------------------------- + -------------------------------- | ___ \2 / 3 3 3 3 | \/ x | /
$$\int \frac{\operatorname{atan}{\left(\frac{x}{2} + x \right)}}{\sqrt{x}}\, dx = C + 2 \sqrt{x} \operatorname{atan}{\left(\frac{x}{2} + x \right)} - \frac{\sqrt{3} \log{\left(- \frac{2 \sqrt{3} \sqrt{x}}{3} + x + \frac{2}{3} \right)}}{3} + \frac{\sqrt{3} \log{\left(\frac{2 \sqrt{3} \sqrt{x}}{3} + x + \frac{2}{3} \right)}}{3} - \frac{2 \sqrt{3} \operatorname{atan}{\left(\sqrt{3} \sqrt{x} - 1 \right)}}{3} - \frac{2 \sqrt{3} \operatorname{atan}{\left(\sqrt{3} \sqrt{x} + 1 \right)}}{3}$$
Use the examples entering the upper and lower limits of integration.