integral of (x^2-5sin(x)+sec^2(x))

Lösung

\int (x^{2} - 5 sin (x) + sec^{2} (x)) d x

\frac{x ^{3}}{3} + 5 cos (x) + tan (x) + C

Schritte zur Lösung

\int x^{2} - 5 sin (x) + sec^{2} (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 x^{2} d x - \int 5 sin (x) d x + \int sec^{2} (x) d x

\int x^{2} d x = \frac{x ^{3}}{3}

\int 5 sin (x) d x = - 5 cos (x)

\int sec^{2} (x) d x = tan (x)

= \frac{x ^{3}}{3} - (- 5 cos (x)) + tan (x)

Vereinfache

= \frac{x ^{3}}{3} + 5 cos (x) + tan (x)

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + 5 cos (x) + tan (x) + C

\int (- 4 x^{6} + 6 x^{4} + 3 x^{3} + 6) d x

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