What is the integral of tan(θ)ln(x)sec(θ) ?

The integral of tan(θ)ln(x)sec(θ) is ln(x)sec(θ)+C

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integral of tan(θ)ln(x)sec(θ)

\int tan (θ) ln (x) sec (θ) d θ

ln (x) sec (θ) + C

Solution steps

\int tan (θ) ln (x) sec (θ) d θ

Take the constant out:

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

= ln (x) \cdot \int sec (θ) tan (θ) d θ

Apply u-substitution

= ln (x) \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= ln (x) \cdot 1 \cdot u

Substitute back

u = sec (θ)

= ln (x) \cdot 1 \cdot sec (θ)

Simplify

= ln (x) sec (θ)

Add a constant to the solution

= ln (x) sec (θ) + C

What is the integral of tan(θ)ln(x)sec(θ) ?
The integral of tan(θ)ln(x)sec(θ) is ln(x)sec(θ)+C