integral of ((e^x))/(sqrt(1-e^{2x))}

解答

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

arcsin (e^{x}) + C

求解步骤

\int \frac{e ^{x}}{1 - e ^{2 x}} d x

使用换元积分法

= \int \frac{1}{1 - u ^{2}} d u

使用积分常见定则:

\int \frac{1}{1 - u ^{2}} d u = arcsin (u)

= arcsin (u)

u = e^{x}

代回

= arcsin (e^{x})

解答补常数

= arcsin (e^{x}) + C

\int_{- 4}^{0} (\frac{y}{4} + y + 5) d y

\int sin^{2} (3 x) cos^{2} (3 x) d x

f (x) = \frac{( 2 x ^{2} + 16 x + x ^{3^{\frac{1}{2}}} + 5 )}{x ^{3}}

\frac{d ^{2} y}{d x ^{2}} - 2 a \frac{d y}{d x} + a^{2} y = 0

\int_{1}^{e} \frac{ln ( z )}{z ^{2}} d z