integral from 1 to 2 of xln((2x)^2)

Lösung

\int_{1}^{2} x ln ((2 x)^{2}) d x

7 ln (2) - \frac{3}{2}

Dezimale

3.35203 \dots

Schritte zur Lösung

\int_{1}^{2} x ln ((2 x)^{2}) d x

Vereinfache

x ln ((2 x)^{2}) : x ln (4 x^{2})

= \int_{1}^{2} x ln (4 x^{2}) d x

Wende die partielle Integration an

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

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

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

\frac{1}{2} x^{2} ln (4 x^{2}) = x^{2} ln (2 x)

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

Berechne die Grenzen:

7 ln (2) - \frac{3}{2}

= 7 ln (2) - \frac{3}{2}

\int_{2}^{6} (\frac{3}{184} x^{2} - \frac{3}{92}) d x

\int_{0}^{l n (12)} tanh (x) d x

\int_{2}^{5} \frac{2}{x} d x

\int_{0}^{1} 1 - x^{2} + \frac{1}{2} x^{4} d x

\int_{3}^{\infty} \frac{1}{2 x - 1} d x