integral from 0 to 4 of x(x^2+2)^2

Lösung

\int_{0}^{4} x (x^{2} + 2)^{2} d x

\frac{2912}{3}

Dezimale

970.66666 \dots

Schritte zur Lösung

\int_{0}^{4} x (x^{2} + 2)^{2} d x

Multipliziere aus

x (x^{2} + 2)^{2} : x^{5} + 4 x^{3} + 4 x

= \int_{0}^{4} x^{5} + 4 x^{3} + 4 x 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_{0}^{4} x^{5} d x + \int_{0}^{4} 4 x^{3} d x + \int_{0}^{4} 4 x d x

\int_{0}^{4} x^{5} d x = \frac{2048}{3}

\int_{0}^{4} 4 x^{3} d x = 256

\int_{0}^{4} 4 x d x = 32

= \frac{2048}{3} + 256 + 32

Vereinfache

\frac{2048}{3} + 256 + 32 : \frac{2912}{3}

= \frac{2912}{3}

\int_{- 1}^{2} 4 - 2 x^{2} + 2 x d x

\int_{1}^{4} (x + x^{2}) d x

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

\int_{0}^{0.4} ln (1 + x^{4}) d x

\int_{- 3}^{2} 9 - x^{2} d x