What is the integral of 1/(xcos^2(1+ln(x))) ?

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

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integral of 1/(xcos^2(1+ln(x)))

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

tan (1 + ln (x)) + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

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

= tan (u)

Substitute back

u = 1 + ln (x)

= tan (1 + ln (x))

Add a constant to the solution

= tan (1 + ln (x)) + C

\int cos (x - 1) d x

\int \frac{3 x + 4}{x ^{2} - 5 x + 6} d x

\int sin (x^{2}) cos (x^{2}) d x

\int \frac{x}{4 x - 2} d x

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

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