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

解答

\int (3 x + 4 x) d x

\frac{3}{4} x^{\frac{4}{3}} + \frac{4}{5} x^{\frac{5}{4}} + C

求解步骤

\int 3 x + 4 x 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 3 x d x + \int 4 x d x

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

\int 4 x d x = \frac{4}{5} x^{\frac{5}{4}}

= \frac{3}{4} x^{\frac{4}{3}} + \frac{4}{5} x^{\frac{5}{4}}

解答补常数

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

d er i v a t i v e y = - x^{2} + 62

\frac{d}{d x} (\frac{cos ( x )}{cos ( x ) + 1})

s im pl i f y \frac{x ^{2} + x + 1}{2 x}

\int \frac{8 x}{8 x + 3} d x

\frac{d}{d x} ((7 - 3 x^{3})^{2})