integral of \sqrt[4]{x^3}+\sqrt[3]{x^4}

解答

\int 4 x^{3} + 3 x^{4} d x

\frac{4}{7} x^{\frac{7}{4}} + \frac{3}{7} x^{\frac{7}{3}} + C

求解步骤

\int 4 x^{3} + 3 x^{4} 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 4 x^{3} d x + \int 3 x^{4} d x

\int 4 x^{3} d x = \frac{4}{7} x^{\frac{7}{4}}

\int 3 x^{4} d x = \frac{3}{7} x^{\frac{7}{3}}

= \frac{4}{7} x^{\frac{7}{4}} + \frac{3}{7} x^{\frac{7}{3}}

解答补常数

= \frac{4}{7} x^{\frac{7}{4}} + \frac{3}{7} x^{\frac{7}{3}} + C

t an g e n t (x + 2)^{2} + (y - 3)^{2} = 37, (- 3, 9)

d er i v a t i v e y = x^{2} + 9

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = \frac{e ^{x}}{1 + x ^{2}}

n \to \infty lim ({(1 + \frac{2}{n})^{4 n}})

d er i v a t i v e y = x^{2} e^{x} - 2 x e^{x} + 9 e^{x}