What is the integral of (xtan(x))/(cos(x)) ?

The integral of (xtan(x))/(cos(x)) is xsec(x)-ln|tan(x)+sec(x)|+C

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integral of (xtan(x))/(cos(x))

\int \frac{x tan ( x )}{cos ( x )} d x

x sec (x) - ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int \frac{x tan ( x )}{cos ( x )} d x

Rewrite using trig identities

= \int x sec (x) tan (x) d x

Apply Integration By Parts

: x sec (x) - \int sec (x) d x

= x sec (x) - \int sec (x) d x

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= x sec (x) - ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= x sec (x) - ln ∣ tan (x) + sec (x) ∣ + C

\int (2 e^{2 x} + 12 x^{3} + 4 x) d x

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

\frac{\partial}{\partial t} (t + sin (t - 1))

\int 3 tan^{3} (2 x) sec^{5} (2 x) d x

x^{3} \cdot y^{^{'}} = x

What is the integral of (xtan(x))/(cos(x)) ?
The integral of (xtan(x))/(cos(x)) is xsec(x)-ln|tan(x)+sec(x)|+C