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Beliebt Rechnen >

integral of-ln(x)-(ln(x))/4

Lösung

\int - ln (x) - \frac{ln ( x )}{4} d x

Lösung

- \frac{5}{4} (x ln (x) - x) + C

Schritte zur Lösung

\int - ln (x) - \frac{ln ( x )}{4} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int ln (x) d x - \int \frac{ln ( x )}{4} d x

\int ln (x) d x = x ln (x) - x

\int \frac{ln ( x )}{4} d x = \frac{1}{4} (x ln (x) - x)

= - (x ln (x) - x) - \frac{1}{4} (x ln (x) - x)

Vereinfache

- (x ln (x) - x) - \frac{1}{4} (x ln (x) - x) : - \frac{5}{4} (x ln (x) - x)

= - \frac{5}{4} (x ln (x) - x)

Füge eine Konstante zur Lösung hinzu

= - \frac{5}{4} (x ln (x) - x) + C

Graph

Beliebte Beispiele

integral from-2 to 4 of |t^2-2t-3|

\int_{- 2}^{4} t^{2} - 2 t - 3 d t

f^'(x)=2x^2+3x-2

f^{^{'}} (x) = 2 x^{2} + 3 x - 2

(\partial)/(\partial x)(x^4y-x^2y^3)

\frac{\partial}{\partial x} (x^{4} y - x^{2} y^{3})

derivative y=3x^2+(4x)/3-2

d er i v a t i v e y = 3 x^{2} + \frac{4 x}{3} - 2

derivative 3/(r^3)

d er i v a t i v e \frac{3}{r ^{3}}