zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的微积分 >

integral of 1/(t^2sqrt(t^2-16))

解答

\int \frac{1}{t ^{2} t ^{2} - 16} d t

解答

\frac{t ^{2} - 16}{16 t} + C

求解步骤

\int \frac{1}{t ^{2} t ^{2} - 16} d t

使用三角换元法

= \int \frac{1}{16 sec ( u )} d u

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{16} \cdot \int \frac{1}{sec ( u )} d u

使用三角恒等式改写

= \frac{1}{16} \cdot \int cos (u) d u

使用积分常见定则:

\int cos (u) d u = sin (u)

= \frac{1}{16} sin (u)

u = arcsec (\frac{1}{4} t)

代回

= \frac{1}{16} sin (arcsec (\frac{1}{4} t))

化简

\frac{1}{16} sin (arcsec (\frac{1}{4} t)) : \frac{t ^{2} - 16}{16 t}

= \frac{t ^{2} - 16}{16 t}

解答补常数

= \frac{t ^{2} - 16}{16 t} + C

作图

流行的例子

derivative of e^{x^2\sqrt[3]{4x-1}}

\frac{d}{d x} (e^{x^{2} 3 4 x - 1})

derivative of e^{x/6}

\frac{d}{d x} (e^{\frac{x}{6}})

integral of 1/(1+e^{-t)}

\int \frac{1}{1 + e ^{- t}} d t

integral of (x^2)/(x^2+81)

\int \frac{x ^{2}}{x ^{2} + 81} d x

(y^'-e^{-t}+5)/y =-5,y(0)=-4

\frac{y ^{^{'}} - e ^{- t} + 5}{y} = - 5, y (0) = - 4