What is the integral of (ln(x))/(sec(c)) ?

The integral of (ln(x))/(sec(c)) is cos(c)(xln(x)-x)+C

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integral of (ln(x))/(sec(c))

\int \frac{ln ( x )}{sec ( c )} d x

cos (c) (x ln (x) - x) + C

Solution steps

\int \frac{ln ( x )}{sec ( c )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{sec ( c )} \cdot \int ln (x) d x

Apply Integration By Parts

: x ln (x) - \int 1 d x

= \frac{1}{sec ( c )} (x ln (x) - \int 1 d x)

\int 1 d x = x

= \frac{1}{sec ( c )} (x ln (x) - x)

Use the basic trigonometric identity:

\frac{1}{sec ( x )} = cos (x)

= cos (c) (x ln (x) - x)

Add a constant to the solution

= cos (c) (x ln (x) - x) + C

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What is the integral of (ln(x))/(sec(c)) ?
The integral of (ln(x))/(sec(c)) is cos(c)(xln(x)-x)+C