integral de e a e^2 de xln(x)

Solução

\int_{e}^{e^{2}} x ln (x) d x

\frac{3 e ^{4} - e ^{2}}{4}

Notação decimal

39.10134 \dots

Passos da solução

\int_{e}^{e^{2}} x ln (x) d x

Aplicar integração por partes

: [\frac{1}{2} (x^{2} ln (x) - 2 \cdot \int \frac{x}{2} d x)]_{e}^{e^{2}}

= [\frac{1}{2} (x^{2} ln (x) - 2 \cdot \int \frac{x}{2} d x)]_{e}^{e^{2}}

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= [\frac{1}{2} (x^{2} ln (x) - 2 \cdot \frac{x ^{2}}{4})]_{e}^{e^{2}}

2 \cdot \frac{x ^{2}}{4} = \frac{x ^{2}}{2}

= [\frac{1}{2} (x^{2} ln (x) - \frac{x ^{2}}{2})]_{e}^{e^{2}}

Calcular os limites:

\frac{3 e ^{4} - e ^{2}}{4}

= \frac{3 e ^{4} - e ^{2}}{4}

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