Sr Examen
Integral de ln(1+t³) dt
Solución
Ha introducido
[src]
3/10 / | | / 3\ | log\1 + t / dt | / 0
$$\int\limits_{0}^{\frac{3}{10}} \log{\left(t^{3} + 1 \right)}\, dt$$
Integral(log(1 + t^3), (t, 0, 3/10))
Respuesta (Indefinida)
[src]
/ | / 2 \ / ___ \ | / 3\ log\1 + t - t/ / 3\ ___ |2*\/ 3 *(-1/2 + t)| | log\1 + t / dt = C - 3*t - --------------- + t*log\1 + t / + \/ 3 *atan|------------------| + log(1 + t) | 2 \ 3 / /
$$\int \log{\left(t^{3} + 1 \right)}\, dt = C + t \log{\left(t^{3} + 1 \right)} - 3 t + \log{\left(t + 1 \right)} - \frac{\log{\left(t^{2} - t + 1 \right)}}{2} + \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(t - \frac{1}{2}\right)}{3} \right)}$$
Gráfica
Respuesta
[src]
/ 79\ /1027\
log|---| 3*log|----| / ___\ ___
9 \100/ \1000/ ___ |2*\/ 3 | pi*\/ 3 /13\
- -- - -------- + ----------- - \/ 3 *atan|-------| + -------- + log|--|
10 2 10 \ 15 / 6 \10/
$$- \frac{9}{10} - \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{15} \right)} + \frac{3 \log{\left(\frac{1027}{1000} \right)}}{10} - \frac{\log{\left(\frac{79}{100} \right)}}{2} + \log{\left(\frac{13}{10} \right)} + \frac{\sqrt{3} \pi}{6}$$
=
=
/ 79\ /1027\
log|---| 3*log|----| / ___\ ___
9 \100/ \1000/ ___ |2*\/ 3 | pi*\/ 3 /13\
- -- - -------- + ----------- - \/ 3 *atan|-------| + -------- + log|--|
10 2 10 \ 15 / 6 \10/
$$- \frac{9}{10} - \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{15} \right)} + \frac{3 \log{\left(\frac{1027}{1000} \right)}}{10} - \frac{\log{\left(\frac{79}{100} \right)}}{2} + \log{\left(\frac{13}{10} \right)} + \frac{\sqrt{3} \pi}{6}$$
-9/10 - log(79/100)/2 + 3*log(1027/1000)/10 - sqrt(3)*atan(2*sqrt(3)/15) + pi*sqrt(3)/6 + log(13/10)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.