What is the integral of 2/(5xsqrt(9-49x^2)) ?

The integral of 2/(5xsqrt(9-49x^2)) is -1/15 (ln|(sqrt(9-49x^2))/3+1|-ln|(sqrt(9-49x^2))/3-1|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2/(5xsqrt(9-49x^2))

\int \frac{2}{5 x 9 - 49 x ^{2}} d x

- \frac{1}{15} (ln \frac{9 - 49 x ^{2}}{3} + 1 - ln \frac{9 - 49 x ^{2}}{3} - 1) + C

Solution steps

\int \frac{2}{5 x 9 - 49 x ^{2}} d x

Take the constant out:

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

= \frac{2}{5} \cdot \int \frac{1}{x 9 - 49 x ^{2}} d x

Apply u-substitution

: \int \frac{1}{2 u 9 - 49 u} d u

= \frac{2}{5} \cdot \int \frac{1}{2 u 9 - 49 u} d u

Take the constant out:

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

= \frac{2}{5} \cdot \frac{1}{2} \cdot \int \frac{1}{u 9 - 49 u} d u

Apply u-substitution

: \int - \frac{2}{- v ^{2} + 9} d v

= \frac{2}{5} \cdot \frac{1}{2} \cdot \int - \frac{2}{- v ^{2} + 9} d v

Take the constant out:

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

= \frac{2}{5} \cdot \frac{1}{2} (- 2 \cdot \int \frac{1}{- v ^{2} + 9} d v)

Apply Integral Substitution

= \frac{2}{5} \cdot \frac{1}{2} (- 2 \cdot \int \frac{1}{3 ( - w ^{2} + 1 )} d w)

Take the constant out:

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

= \frac{2}{5} \cdot \frac{1}{2} (- 2 \cdot \frac{1}{3} \cdot \int \frac{1}{- w ^{2} + 1} d w)

Use the common integral:

\int \frac{1}{- w ^{2} + 1} d w = \frac{ln ∣ w + 1 ∣}{2} - \frac{ln ∣ w - 1 ∣}{2}

= \frac{2}{5} \cdot \frac{1}{2} (- 2 \cdot \frac{1}{3} (\frac{ln ∣ w + 1 ∣}{2} - \frac{ln ∣ w - 1 ∣}{2}))

Substitute back

= \frac{2}{5} \cdot \frac{1}{2} - 2 \cdot \frac{1}{3} \frac{ln \frac{9 - 49 x ^{2}}{3} + 1}{2} - \frac{ln \frac{9 - 49 x ^{2}}{3} - 1}{2}

Simplify

\frac{2}{5} \cdot \frac{1}{2} - 2 \cdot \frac{1}{3} \frac{ln \frac{9 - 49 x ^{2}}{3} + 1}{2} - \frac{ln \frac{9 - 49 x ^{2}}{3} - 1}{2} : - \frac{1}{15} (ln \frac{9 - 49 x ^{2}}{3} + 1 - ln \frac{9 - 49 x ^{2}}{3} - 1)

= - \frac{1}{15} (ln \frac{9 - 49 x ^{2}}{3} + 1 - ln \frac{9 - 49 x ^{2}}{3} - 1)

Add a constant to the solution

= - \frac{1}{15} (ln \frac{9 - 49 x ^{2}}{3} + 1 - ln \frac{9 - 49 x ^{2}}{3} - 1) + C

\frac{d x}{d t} = sin (2 t) - 3 x

\frac{\partial}{\partial y} (sin (y) - x y + y^{2})

\int \frac{1}{( x + 2 ) x ^{2} + 4 x + 3} d x

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

3 x^{2}, 6 x

What is the integral of 2/(5xsqrt(9-49x^2)) ?
The integral of 2/(5xsqrt(9-49x^2)) is -1/15 (ln|(sqrt(9-49x^2))/3+1|-ln|(sqrt(9-49x^2))/3-1|)+C