What is the integral of 1/(sqrt(12+x^2)) ?

The integral of 1/(sqrt(12+x^2)) is ln(1/(2sqrt(3))|x+sqrt(12+x^2)|)+C

Popular >

integral of 1/(sqrt(12+x^2))

\int \frac{1}{12 + x ^{2}} d x

ln (\frac{1}{2 3} x + 12 + x^{2}) + C

Solution steps

\int \frac{1}{12 + 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}{2 3} x)

= ln tan (arctan (\frac{1}{2 3} x)) + sec (arctan (\frac{1}{2 3} x))

Simplify

ln tan (arctan (\frac{1}{2 3} x)) + sec (arctan (\frac{1}{2 3} x)) : ln (\frac{1}{2 3} x + 12 + x^{2})

= ln (\frac{1}{2 3} x + 12 + x^{2})

Add a constant to the solution

= ln (\frac{1}{2 3} x + 12 + x^{2}) + C

\int \frac{( ln ( x ) + 1 ) ^{2}}{x ln ( x )} d x

\int \frac{x + 2}{e ^{x}} d x

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

\int sin (38 t) sec^{2} (cos (38 t)) d t

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

What is the integral of 1/(sqrt(12+x^2)) ?
The integral of 1/(sqrt(12+x^2)) is ln(1/(2sqrt(3))|x+sqrt(12+x^2)|)+C