What is the integral of (x-1)sec^2(x) ?

The integral of (x-1)sec^2(x) is tan(x)(x-1)+ln|cos(x)|+C

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integral of (x-1)sec^2(x)

\int (x - 1) sec^{2} (x) d x

tan (x) (x - 1) + ln ∣ cos (x) ∣ + C

Solution steps

\int (x - 1) sec^{2} (x) d x

Apply Integration By Parts

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

= tan (x) (x - 1) - \int tan (x) d x

\int tan (x) d x = - ln ∣ cos (x) ∣

= tan (x) (x - 1) - (- ln ∣ cos (x) ∣)

Simplify

= tan (x) (x - 1) + ln ∣ cos (x) ∣

Add a constant to the solution

= tan (x) (x - 1) + ln ∣ cos (x) ∣ + C

(x - 1) ln (x)

\frac{\partial}{\partial x} (\frac{1}{3 x + 2})

x \to 2 - lim (g (x))

\int \frac{x}{2 x ^{2} + 1} d x

x \to \infty lim (f (x) x)

What is the integral of (x-1)sec^2(x) ?
The integral of (x-1)sec^2(x) is tan(x)(x-1)+ln|cos(x)|+C