What is the integral of 1/(xcos(ln(x))) ?

The integral of 1/(xcos(ln(x))) is ln|tan(ln(x))+sec(ln(x))|+C

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integral of 1/(xcos(ln(x)))

\int \frac{1}{x cos ( ln ( x ) )} d x

ln ∣ tan (ln (x)) + sec (ln (x)) ∣ + C

Solution steps

\int \frac{1}{x cos ( ln ( x ) )} d x

Apply u-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 = ln (x)

= ln ∣ tan (ln (x)) + sec (ln (x)) ∣

Add a constant to the solution

= ln ∣ tan (ln (x)) + sec (ln (x)) ∣ + C

x \to - 2 + lim (\frac{x ^{2}}{x + 2})

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\frac{\partial}{\partial x} (x^{9} y^{9} - x^{8} y^{8})

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What is the integral of 1/(xcos(ln(x))) ?
The integral of 1/(xcos(ln(x))) is ln|tan(ln(x))+sec(ln(x))|+C