What is the integral of 1/(sqrt(576+x^2)) ?

The integral of 1/(sqrt(576+x^2)) is ln(1/24 |x+sqrt(576+x^2)|)+C

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integral of 1/(sqrt(576+x^2))

\int \frac{1}{576 + x ^{2}} d x

ln (\frac{1}{24} x + 576 + x^{2}) + C

Solution steps

\int \frac{1}{576 + 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}{24} x)

= ln tan (arctan (\frac{1}{24} x)) + sec (arctan (\frac{1}{24} x))

Simplify

ln tan (arctan (\frac{1}{24} x)) + sec (arctan (\frac{1}{24} x)) : ln (\frac{1}{24} x + 576 + x^{2})

= ln (\frac{1}{24} x + 576 + x^{2})

Add a constant to the solution

= ln (\frac{1}{24} x + 576 + x^{2}) + C

\int arcsin^{2} (x) d x

\int \frac{1}{x ^{2} + 6 x + 25} d x

\int \frac{9 x ^{2} - 6}{x ^{2}} d x

\frac{\partial}{\partial x} (\frac{- 8 x + 5}{2 y ^{2} + 1})

y^{^{'}} + \frac{1}{x} y = 7 x^{2}

What is the integral of 1/(sqrt(576+x^2)) ?
The integral of 1/(sqrt(576+x^2)) is ln(1/24 |x+sqrt(576+x^2)|)+C