integral of tan(x)+x^2

解答

\int tan (x) + x^{2} d x

- ln ∣ cos (x) ∣ + \frac{x ^{3}}{3} + C

求解步骤

\int tan (x) + x^{2} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int tan (x) d x = - ln ∣ cos (x) ∣

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

= - ln ∣ cos (x) ∣ + \frac{x ^{3}}{3}

解答补常数

= - ln ∣ cos (x) ∣ + \frac{x ^{3}}{3} + C

\int \frac{1}{7 + x} d x

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\int 14 e^{u} d u