Solve \int _ { e ^ { 2 } } ^ { e ^ { 3 } } \frac { d

Calcule

\int_{e^{2}}^{e^{3}} \frac{1}{x ( ln ( x ) - 1 )} d x

Multiplique os termos

Langkah Lebih Banyak

\int_{e^{2}}^{e^{3}} \frac{1}{x ln ( x ) - x} d x

Avalie o integral

\int \frac{1}{x ln ( x ) - x} d x

Reescrever a expressão

\int \frac{1}{x ( ln ( x ) - 1 )} d x

Use a substitui \overset{c}{¸} \overset{a}{˜} o d x = x d t para transformar o integral

Langkah Lebih Banyak

\int \frac{1}{x ( ln ( x ) - 1 )} \times x d t

Simplificar

Langkah Lebih Banyak

\int \frac{1}{ln ( x ) - 1} d t

Use a substitui \overset{c}{¸} \overset{a}{˜} o t = ln (x) para transformar o integral

\int \frac{1}{t - 1} d t

Use a propriedade da integral \int \frac{1}{a x + b} d x = \frac{1}{a} ln ∣ a x + b ∣

ln (∣ t - 1 ∣)

Substituir de volta

ln (∣ ln (x) - 1 ∣)

Devolva os limites

(ln (∣ ln (x) - 1 ∣))_{e^{2}}^{e^{3}}

Larutan

Langkah Lebih Banyak

ln (2)

Formulário Alternativo

\approx 0.693147

\int _ { e ^ { 2 } } ^ { e ^ { 3 } } \frac { d x } { x ( \ln x 1 ) }