Sr Examen
Integral de ln(1+x)/(x*sqrt(x)) dx
Solución
Ha introducido
[src]
oo / | | log(1 + x) | ---------- dx | ___ | x*\/ x | / 2
$$\int\limits_{2}^{\infty} \frac{\log{\left(x + 1 \right)}}{\sqrt{x} x}\, dx$$
Integral(log(1 + x)/((x*sqrt(x))), (x, 2, oo))
Respuesta (Indefinida)
[src]
/ | | log(1 + x) / 1 \ 2*log(1 + x) | ---------- dx = C - 4*atan|-----| - ------------ | ___ | ___| ___ | x*\/ x \\/ x / \/ x | /
$$\int \frac{\log{\left(x + 1 \right)}}{\sqrt{x} x}\, dx = C - 4 \operatorname{atan}{\left(\frac{1}{\sqrt{x}} \right)} - \frac{2 \log{\left(x + 1 \right)}}{\sqrt{x}}$$
Respuesta
[src]
/ / ___\\
___ | ___ |\/ 2 ||
\/ 2 *|2*log(2) + 2*log(3/2) + 4*\/ 2 *atan|-----||
\ \ 2 //
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2
$$\frac{\sqrt{2} \left(2 \log{\left(\frac{3}{2} \right)} + 2 \log{\left(2 \right)} + 4 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}\right)}{2}$$
=
=
/ / ___\\
___ | ___ |\/ 2 ||
\/ 2 *|2*log(2) + 2*log(3/2) + 4*\/ 2 *atan|-----||
\ \ 2 //
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2
$$\frac{\sqrt{2} \left(2 \log{\left(\frac{3}{2} \right)} + 2 \log{\left(2 \right)} + 4 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}\right)}{2}$$
sqrt(2)*(2*log(2) + 2*log(3/2) + 4*sqrt(2)*atan(sqrt(2)/2))/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.