What is the integral of 1/(sqrt(144+x^2)) ?

The integral of 1/(sqrt(144+x^2)) is ln(1/12 |x+sqrt(144+x^2)|)+C

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integral of 1/(sqrt(144+x^2))

\int \frac{1}{144 + x ^{2}} d x

ln (\frac{1}{12} x + 144 + x^{2}) + C

Solution steps

\int \frac{1}{144 + 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}{12} x)

= ln tan (arctan (\frac{1}{12} x)) + sec (arctan (\frac{1}{12} x))

Simplify

ln tan (arctan (\frac{1}{12} x)) + sec (arctan (\frac{1}{12} x)) : ln (\frac{1}{12} x + 144 + x^{2})

= ln (\frac{1}{12} x + 144 + x^{2})

Add a constant to the solution

= ln (\frac{1}{12} x + 144 + x^{2}) + C

sin (3 x) + cos (4 x)

\int_{0}^{1} \frac{1}{x ^{0.5}} d x

\frac{\partial}{\partial x} ((3 x + 1) y)

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

y^{^{''}} - 10 y^{^{'}} + 34 y = 0, y (0) = - 2, y^{^{'}} (0) = - 3

What is the integral of 1/(sqrt(144+x^2)) ?
The integral of 1/(sqrt(144+x^2)) is ln(1/12 |x+sqrt(144+x^2)|)+C