integral of (sqrt(49-y^8))/(y^5)

解答

\int \frac{49 - y ^{8}}{y ^{5}} d y

- \frac{49 - y ^{8}}{4 y ^{4}} - \frac{1}{4} arcsin (\frac{1}{7} y^{4}) + C

求解步骤

\int \frac{49 - y ^{8}}{y ^{5}} d y

使用分布积分法

= - \frac{49 - y ^{8}}{4 y ^{4}} - \int \frac{y ^{3}}{49 - y ^{8}} d y

\int \frac{y ^{3}}{49 - y ^{8}} d y = \frac{1}{4} arcsin (\frac{1}{7} y^{4})

= - \frac{49 - y ^{8}}{4 y ^{4}} - \frac{1}{4} arcsin (\frac{1}{7} y^{4})

解答补常数

= - \frac{49 - y ^{8}}{4 y ^{4}} - \frac{1}{4} arcsin (\frac{1}{7} y^{4}) + C

\frac{d}{d x} (40 x - 4 x)

\int \frac{1}{( x ^{2} + 16 ) ^{\frac{3}{2}}} d x

t an g e n t f (x) = x^{2} - 3, at x = 3

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

x \to \infty lim (4 e^{- 4 x})