What is the integral from-1 to 3 of x/(10-x^2) ?

The integral from-1 to 3 of x/(10-x^2) is ln(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 3 of x/(10-x^2)

\int_{- 1}^{3} \frac{x}{10 - x ^{2}} d x

ln (3)

Decimal Notation

1.09861 \dots

Solution steps

\int_{- 1}^{3} \frac{x}{10 - x ^{2}} d x

Apply u-substitution

: \int_{9}^{1} - \frac{1}{2 u} d u

= \int_{9}^{1} - \frac{1}{2 u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{9} - \frac{1}{2 u} d u

Take the constant out:

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

= - (- \frac{1}{2} \cdot \int_{1}^{9} \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- \frac{1}{2} [ln ∣ u ∣]_{1}^{9})

Simplify

= \frac{1}{2} [ln ∣ u ∣]_{1}^{9}

Compute the boundaries:

2 ln (3)

= \frac{1}{2} \cdot 2 ln (3)

Simplify

= ln (3)

\int_{1}^{4} \frac{8 ( ln ( x ) ) ^{3}}{x} d x

\int_{\frac{1}{2}}^{2} ∣ ln (x) ∣ d x

\int_{\frac{1}{2}}^{1} (x^{- 3} - 11) d x

\int_{1}^{4} x + 1 d x

\int_{x}^{2 - x} 6 x^{2} y d y

What is the integral from-1 to 3 of x/(10-x^2) ?
The integral from-1 to 3 of x/(10-x^2) is ln(3)