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Beliebt Rechnen >

integral of (x^6)/(sqrt(x^{14)-3)}

Lösung

\int \frac{x ^{6}}{x ^{14} - 3} d x

Lösung

\frac{1}{7} ln \frac{1}{3} (x^{14} - 3) + \frac{1}{3} x^{7} + C

Schritte zur Lösung

\int \frac{x ^{6}}{x ^{14} - 3} d x

Wende U-Substitution an

= \int \frac{1}{7 u ^{2} - 3} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{7} \cdot \int \frac{1}{u ^{2} - 3} d u

Trigonometrische Substitution anwenden

= \frac{1}{7} \cdot \int sec (v) d v

Nutze das gemeinsame Integral :

\int sec (v) d v = ln ∣ tan (v) + sec (v) ∣

= \frac{1}{7} ln ∣ tan (v) + sec (v) ∣

Ersetze zurück

= \frac{1}{7} ln tan (arcsec (\frac{1}{3} x^{7})) + sec (arcsec (\frac{1}{3} x^{7}))

Vereinfache

\frac{1}{7} ln tan (arcsec (\frac{1}{3} x^{7})) + sec (arcsec (\frac{1}{3} x^{7})) : \frac{1}{7} ln \frac{1}{3} (x^{14} - 3) + \frac{1}{3} x^{7}

= \frac{1}{7} ln \frac{1}{3} (x^{14} - 3) + \frac{1}{3} x^{7}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{7} ln \frac{1}{3} (x^{14} - 3) + \frac{1}{3} x^{7} + C

Graph

Beliebte Beispiele

slopeintercept (0,3),(1,5)

s l o p e in t erce pt (0, 3), (1, 5)

limit as x approaches 6 of 7

x \to 6 lim (7)

integral of (sin(x))/((3+cos(x))^2)

\int \frac{sin ( x )}{( 3 + cos ( x ) ) ^{2}} d x

integral from 0 to b of 1/(sqrt(4-x^2))

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

tangent y=7cos(x),\at x= pi/3

t an g e n t y = 7 cos (x), at x = \frac{π}{3}