What is the integral of u*sec^2(u) ?

The integral of u*sec^2(u) is utan(u)+ln|cos(u)|+C

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integral of u*sec^2(u)

\int u \cdot sec^{2} (u) d u

u tan (u) + ln ∣ cos (u) ∣ + C

Solution steps

\int u sec^{2} (u) d u

Apply Integration By Parts

: u tan (u) - \int tan (u) d u

= u tan (u) - \int tan (u) d u

\int tan (u) d u = - ln ∣ cos (u) ∣

= u tan (u) - (- ln ∣ cos (u) ∣)

Simplify

= u tan (u) + ln ∣ cos (u) ∣

Add a constant to the solution

= u tan (u) + ln ∣ cos (u) ∣ + C

f (x) = 8 x^{3}

\frac{d}{d x} ((sec^{2} (x)) d x)

f (t) = t^{6} sin (t)

cos (- x)

\frac{\partial}{\partial y} (5 x + 4 y)

What is the integral of u*sec^2(u) ?
The integral of u*sec^2(u) is utan(u)+ln|cos(u)|+C