What is the integral of 1/(ycos^2(ln(y))) ?

The integral of 1/(ycos^2(ln(y))) is tan(ln(y))+C

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integral of 1/(ycos^2(ln(y)))

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

tan (ln (y)) + C

Solution steps

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

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 (y)

= tan (ln (y))

Add a constant to the solution

= tan (ln (y)) + C

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What is the integral of 1/(ycos^2(ln(y))) ?
The integral of 1/(ycos^2(ln(y))) is tan(ln(y))+C