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Beliebt Rechnen >

integral from x^3 to x^4 of (2t-1)^3

Lösung

\int_{x^{3}}^{x^{4}} (2 t - 1)^{3} d t

Lösung

x^{3} (2 x^{13} - 6 x^{9} + 4 x^{6} + 3 x^{5} - 3 x^{3} - x + 1)

Schritte zur Lösung

\int_{x^{3}}^{x^{4}} (2 t - 1)^{3} d t

Wende U-Substitution an

= \int_{2 x^{3} - 1}^{2 x^{4} - 1} \frac{u ^{3}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{2 x^{3} - 1}^{2 x^{4} - 1} u^{3} d u

Wende die Potenzregel an

= \frac{1}{2} [\frac{u ^{4}}{4}]_{2 x^{3} - 1}^{2 x^{4} - 1}

Berechne die Grenzen:

\frac{( 2 x ^{4} - 1 ) ^{4}}{4} - \frac{( 2 x ^{3} - 1 ) ^{4}}{4}

= \frac{1}{2} (\frac{( 2 x ^{4} - 1 ) ^{4}}{4} - \frac{( 2 x ^{3} - 1 ) ^{4}}{4})

Vereinfache

= x^{3} (2 x^{13} - 6 x^{9} + 4 x^{6} + 3 x^{5} - 3 x^{3} - x + 1)

Beliebte Beispiele

integral of (sqrt(3))

\int (3) d x

derivative f(x)=(60)/(0.01x^2+1)

d er i v a t i v e f (x) = \frac{60}{0.01 x ^{2} + 1}

derivative of arctan(x^2+1)

\frac{d}{d x} (arctan (x^{2} + 1))

sum from n=1 to infinity of (50)/(5^n)

n = 1 \sum \infty \frac{50}{5 ^{n}}

derivative e^{ln(sec(2x))}

d er i v a t i v e e^{l n (s e c (2 x))}