What is the integral of 1/(x*cos^2(ln(x))) ?

The integral of 1/(x*cos^2(ln(x))) is tan(ln(x))+C

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integral of 1/(x*cos^2(ln(x)))

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

tan (ln (x)) + C

Solution steps

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

Apply u-substitution

= \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= tan (u)

Substitute back

u = ln (x)

= tan (ln (x))

Add a constant to the solution

= tan (ln (x)) + C

What is the integral of 1/(x*cos^2(ln(x))) ?
The integral of 1/(x*cos^2(ln(x))) is tan(ln(x))+C