integral from 1 to e of ln(x^4)

Lösung

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

4

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int 4 d x = 4 x

= [x ln (x^{4}) - 4 x]_{1}^{e}

Wende log Regel an

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

angenommen

x \geq 0

= [4 x ln (x) - 4 x]_{1}^{e}

Berechne die Grenzen:

4

= 4

\int_{0}^{3} x^{2} - 6 x + 8 d x

\int_{0}^{3} t^{2} d t

\int_{0}^{4} 8 y d y

\int_{i}^{1} (z + 1)^{2} d z

\int_{1}^{\infty} \frac{1}{n ^{2} + 1}