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

The integral of sec(x)tan(x)(x/pi) is 1/pi (xsec(x)-ln|tan(x)+sec(x)|)+C

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integral of sec(x)tan(x)(x/pi)

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

\frac{1}{π} (x sec (x) - ln ∣ tan (x) + sec (x) ∣) + C

Solution steps

\int sec (x) tan (x) \frac{x}{π} d x

Take the constant out:

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

= \frac{1}{π} \cdot \int sec (x) tan (x) x d x

Apply Integration By Parts

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

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

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

= \frac{1}{π} (x sec (x) - ln ∣ tan (x) + sec (x) ∣)

Add a constant to the solution

= \frac{1}{π} (x sec (x) - ln ∣ tan (x) + sec (x) ∣) + C

\frac{d y}{d t} + y = cos (2 t), y (0) = 5

\frac{d y}{d x} = \frac{1}{x y}

f (x) = x x^{3} - 6

y = 2 x^{2} 2 - x

\frac{\partial}{\partial x} (e^{- 1} cos (π x))

What is the integral of sec(x)tan(x)(x/pi) ?
The integral of sec(x)tan(x)(x/pi) is 1/pi (xsec(x)-ln|tan(x)+sec(x)|)+C