What is the integral of 1/(169-16x^2) ?

The integral of 1/(169-16x^2) is 1/104 (ln| 4/13 x+1|-ln| 4/13 x-1|)+C

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integral of 1/(169-16x^2)

\int \frac{1}{169 - 16 x ^{2}} d x

\frac{1}{104} (ln \frac{4}{13} x + 1 - ln \frac{4}{13} x - 1) + C

Solution steps

\int \frac{1}{169 - 16 x ^{2}} d x

Apply Integral Substitution

= \int \frac{1}{52 ( - 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}{52} \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}{52} (\frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2})

Substitute back

u = \frac{4}{13} x

= \frac{1}{52} (\frac{ln \frac{4}{13} x + 1}{2} - \frac{ln \frac{4}{13} x - 1}{2})

Simplify

\frac{1}{52} (\frac{ln \frac{4}{13} x + 1}{2} - \frac{ln \frac{4}{13} x - 1}{2}) : \frac{1}{104} (ln \frac{4}{13} x + 1 - ln \frac{4}{13} x - 1)

= \frac{1}{104} (ln \frac{4}{13} x + 1 - ln \frac{4}{13} x - 1)

Add a constant to the solution

= \frac{1}{104} (ln \frac{4}{13} x + 1 - ln \frac{4}{13} x - 1) + C

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

t y^{^{''}} + 4 y^{^{'}} = t^{2}

f f^{^{'}} (xx) = x x^{3} - x x^{2} - 6 xx

\frac{d}{d x} (e^{c o s h (x)} cos^{2} (x))

\int_{0}^{7} - 30 x^{2} + 420 x d x

What is the integral of 1/(169-16x^2) ?
The integral of 1/(169-16x^2) is 1/104 (ln| 4/13 x+1|-ln| 4/13 x-1|)+C