What is the integral of 1/(441-400x^2) ?

The integral of 1/(441-400x^2) is 1/840 (ln| 20/21 x+1|-ln| 20/21 x-1|)+C

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integral of 1/(441-400x^2)

\int \frac{1}{441 - 400 x ^{2}} d x

\frac{1}{840} (ln \frac{20}{21} x + 1 - ln \frac{20}{21} x - 1) + C

Solution steps

\int \frac{1}{441 - 400 x ^{2}} d x

Apply Integral Substitution

= \int \frac{1}{420 ( - u ^{2} + 1 )} d u

Take the constant out:

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

= \frac{1}{420} \cdot \int \frac{1}{- u ^{2} + 1} d u

Use the common integral:

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

= \frac{1}{420} (\frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2})

Substitute back

u = \frac{20}{21} x

= \frac{1}{420} (\frac{ln \frac{20}{21} x + 1}{2} - \frac{ln \frac{20}{21} x - 1}{2})

Simplify

\frac{1}{420} (\frac{ln \frac{20}{21} x + 1}{2} - \frac{ln \frac{20}{21} x - 1}{2}) : \frac{1}{840} (ln \frac{20}{21} x + 1 - ln \frac{20}{21} x - 1)

= \frac{1}{840} (ln \frac{20}{21} x + 1 - ln \frac{20}{21} x - 1)

Add a constant to the solution

= \frac{1}{840} (ln \frac{20}{21} x + 1 - ln \frac{20}{21} x - 1) + C

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

x^{3} - 6 x^{2} + 8 x, x^{2} - 4 x

t^{4} y^{^{''}} + t^{3} y^{^{'}} = 0

\int \frac{2}{π ( 1 + x ^{2} )} d x

\int \frac{- x ^{2} + 11 x - 18}{x ^{2}} d x

What is the integral of 1/(441-400x^2) ?
The integral of 1/(441-400x^2) is 1/840 (ln| 20/21 x+1|-ln| 20/21 x-1|)+C