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/(sqrt(x^2-4x-3))

解答

\int \frac{1}{x ^{2} - 4 x - 3} d x

解答

ln \frac{1}{7} (x^{2} - 4 x - 3) + \frac{1}{7} (x - 2) + C

求解步骤

\int \frac{1}{x ^{2} - 4 x - 3} d x

对

x^{2} - 4 x - 3

配方:

(x - 2)^{2} - 7

= \int \frac{1}{( x - 2 ) ^{2} - 7} d x

使用换元积分法

= \int \frac{1}{u ^{2} - 7} d u

使用三角换元法

= \int sec (v) d v

使用积分常见定则:

\int sec (v) d v = ln ∣ tan (v) + sec (v) ∣

= ln ∣ tan (v) + sec (v) ∣

代回

= ln tan (arcsec (\frac{1}{7} (x - 2))) + sec (arcsec (\frac{1}{7} (x - 2)))

化简

ln tan (arcsec (\frac{1}{7} (x - 2))) + sec (arcsec (\frac{1}{7} (x - 2))) : ln \frac{1}{7} (x^{2} - 4 x - 3) + \frac{1}{7} (x - 2)

= ln \frac{1}{7} (x^{2} - 4 x - 3) + \frac{1}{7} (x - 2)

解答补常数

= ln \frac{1}{7} (x^{2} - 4 x - 3) + \frac{1}{7} (x - 2) + C

作图

流行的例子

integral of (2x^2)/((x^2+5)^2)

\int \frac{2 x ^{2}}{( x ^{2} + 5 ) ^{2}} d x

integral of ((2+ln(x))^3)/x

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

积分 cos^2(t)

in t e g r a l cos^{2} (t)

integral of sqrt(1/2)

\int \frac{1}{2}

integral of sin(ax)e^{bx+c}

\int sin (a x) e^{b x + c} d x