integral from-1 to 0 of (x^{15})/(x^8+1)

Lösung

\int_{- 1}^{0} \frac{x ^{15}}{x ^{8} + 1} d x

- \frac{1}{8} + \frac{1}{8} ln (2)

Dezimale

- 0.03835 \dots

Schritte zur Lösung

\int_{- 1}^{0} \frac{x ^{15}}{x ^{8} + 1} d x

Lange Division

\frac{x ^{15}}{x ^{8} + 1} : x^{7} - \frac{x ^{7}}{x ^{8} + 1}

= \int_{- 1}^{0} x^{7} - \frac{x ^{7}}{x ^{8} + 1} 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_{- 1}^{0} x^{7} d x - \int_{- 1}^{0} \frac{x ^{7}}{x ^{8} + 1} d x

\int_{- 1}^{0} x^{7} d x = - \frac{1}{8}

\int_{- 1}^{0} \frac{x ^{7}}{x ^{8} + 1} d x = - \frac{1}{8} ln (2)

= - \frac{1}{8} - (- \frac{1}{8} ln (2))

Vereinfache

= - \frac{1}{8} + \frac{1}{8} ln (2)

\int_{- 2}^{2} (x^{6} - 3 x^{2}) d x

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

\int_{0}^{4} \frac{x}{8 - x} d x

\int_{0}^{1} \frac{1}{x ^{3} - 5 x ^{2}} d x

\int_{0}^{2 π} \frac{1}{2 + cos ( x )} d x