integral of 5+2/3 x^2+3/4 x^3

解答

\int 5 + \frac{2}{3} x^{2} + \frac{3}{4} x^{3} d x

5 x + \frac{2 x ^{3}}{9} + \frac{3 x ^{4}}{16} + C

求解步骤

\int 5 + \frac{2}{3} x^{2} + \frac{3}{4} x^{3} 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 5 d x + \int \frac{2}{3} x^{2} d x + \int \frac{3}{4} x^{3} d x

\int 5 d x = 5 x

\int \frac{2}{3} x^{2} d x = \frac{2 x ^{3}}{9}

\int \frac{3}{4} x^{3} d x = \frac{3 x ^{4}}{16}

= 5 x + \frac{2 x ^{3}}{9} + \frac{3 x ^{4}}{16}

解答补常数

= 5 x + \frac{2 x ^{3}}{9} + \frac{3 x ^{4}}{16} + C

\int (4 sin (x) + 5 sinh (x)) d x

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