integral of (x^4)^{1/2}

解答

\int (x^{4})^{\frac{1}{2}} d x

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

求解步骤

\int (x^{4})^{\frac{1}{2}} d x

(x^{4})^{\frac{1}{2}} = x^{2},

假定

x \geq 0

= \int x^{2} d x

使用幂法则

= \frac{x ^{3}}{3}

解答补常数

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

h \to \frac{π}{2} lim (\frac{( 1 - cos ( 3 h ) )}{h})

\int \frac{z ^{3}}{3 z ^{2} + 1} d z

\int x csc (x^{2}) d x

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 e^{3 t}, y (0) = 0, y^{^{'}} (0) = 4

\frac{d}{d x} (x - ln (e^{x} cos (x)))