What is the integral of 1/(sqrt(484+x^2)) ?

The integral of 1/(sqrt(484+x^2)) is ln(1/22 |x+sqrt(484+x^2)|)+C

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integral of 1/(sqrt(484+x^2))

\int \frac{1}{484 + x ^{2}} d x

ln (\frac{1}{22} x + 484 + x^{2}) + C

Solution steps

\int \frac{1}{484 + x ^{2}} d x

Apply Trigonometric Substitution

: \int sec (u) d u

= \int sec (u) d u

Use the common integral:

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

= ln ∣ tan (u) + sec (u) ∣

Substitute back

u = arctan (\frac{1}{22} x)

= ln tan (arctan (\frac{1}{22} x)) + sec (arctan (\frac{1}{22} x))

Simplify

ln tan (arctan (\frac{1}{22} x)) + sec (arctan (\frac{1}{22} x)) : ln (\frac{1}{22} x + 484 + x^{2})

= ln (\frac{1}{22} x + 484 + x^{2})

Add a constant to the solution

= ln (\frac{1}{22} x + 484 + x^{2}) + C

5 \frac{d y}{d x} + 45 y = 9

\frac{d}{d x} (x^{2} cos (y) y^{^{'}})

f (x) = 2 cos (3 x)

\frac{d}{d x} (1 - e^{2 x})

y^{^{''}} + 3 y^{^{'}} - 28 y = 0

What is the integral of 1/(sqrt(484+x^2)) ?
The integral of 1/(sqrt(484+x^2)) is ln(1/22 |x+sqrt(484+x^2)|)+C