integral from x to 2x^2 of ln(t)

Lösung

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

2 ln (2) x^{2} + 4 x^{2} ln (x) - 2 x^{2} - x ln (x) + x

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int 1 d t = t

= [t ln (t) - t]_{x}^{2 x^{2}}

Berechne die Grenzen:

2 ln (2) x^{2} + 4 x^{2} ln (x) - 2 x^{2} - x ln (x) + x

= 2 ln (2) x^{2} + 4 x^{2} ln (x) - 2 x^{2} - x ln (x) + x

\int_{- 2}^{2} 3 x^{2} + 2 x d x

\int_{0}^{1} (4 x^{3} + 5) d x

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

\int_{0}^{3} \frac{x}{1 + x} d x

\int_{0}^{1} ∣ x ∣ - x^{2} d x