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

The integral of x/(sec(x)) is xsin(x)+cos(x)+C

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integral of x/(sec(x))

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

x sin (x) + cos (x) + C

Solution steps

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

Rewrite using trig identities

= \int x cos (x) d x

Apply Integration By Parts

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

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

\int sin (x) d x = - cos (x)

= x sin (x) - (- cos (x))

Simplify

= x sin (x) + cos (x)

Add a constant to the solution

= x sin (x) + cos (x) + C

\frac{d y}{d x}, y^{x} = x^{y}

\frac{d y}{d t} - y = 1, y (0) = 0

t y^{^{'}} + y = 1 + y + y^{2}

\frac{d}{d x} (f (x) + g (x))

\frac{d}{d x} (x^{m})

What is the integral of x/(sec(x)) ?
The integral of x/(sec(x)) is xsin(x)+cos(x)+C