Sr Examen
Integral de (sqrt(x))((ln(x))/(ln(2))) dx
Solución
Ha introducido
[src]
4 / | | ___ log(x) | \/ x *------ dx | log(2) | / 1
$$\int\limits_{1}^{4} \sqrt{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\, dx$$
Integral(sqrt(x)*(log(x)/log(2)), (x, 1, 4))
Respuesta (Indefinida)
[src]
/ 3/2 3/2 \ / | 2*x x *log(x)| | 2*|- ------ + -----------| | ___ log(x) \ 9 3 / | \/ x *------ dx = C + -------------------------- | log(2) log(2) | /
$$\int \sqrt{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\, dx = C + \frac{2 \left(\frac{x^{\frac{3}{2}} \log{\left(x \right)}}{3} - \frac{2 x^{\frac{3}{2}}}{9}\right)}{\log{\left(2 \right)}}$$
Respuesta
[src]
32 16*log(4)
- -- + ---------
4 9 3
-------- + ----------------
9*log(2) log(2)
$$\frac{4}{9 \log{\left(2 \right)}} + \frac{- \frac{32}{9} + \frac{16 \log{\left(4 \right)}}{3}}{\log{\left(2 \right)}}$$
=
=
32 16*log(4)
- -- + ---------
4 9 3
-------- + ----------------
9*log(2) log(2)
$$\frac{4}{9 \log{\left(2 \right)}} + \frac{- \frac{32}{9} + \frac{16 \log{\left(4 \right)}}{3}}{\log{\left(2 \right)}}$$
4/(9*log(2)) + (-32/9 + 16*log(4)/3)/log(2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.