What is the integral of 12xsec^2(x) ?

The integral of 12xsec^2(x) is 12(xtan(x)+ln|cos(x)|)+C

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integral of 12xsec^2(x)

\int 12 x sec^{2} (x) d x

12 (x tan (x) + ln ∣ cos (x) ∣) + C

Solution steps

\int 12 x sec^{2} (x) d x

Take the constant out:

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

= 12 \cdot \int x sec^{2} (x) d x

Apply Integration By Parts

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

= 12 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 12 (x tan (x) - (- ln ∣ cos (x) ∣))

Simplify

= 12 (x tan (x) + ln ∣ cos (x) ∣)

Add a constant to the solution

= 12 (x tan (x) + ln ∣ cos (x) ∣) + C

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

(x^{4} + 3 x)^{- 1}

\int_{0}^{\frac{π}{2}} 1 d θ

\frac{d}{d x} (x^{2} + \frac{3456}{x})

What is the integral of 12xsec^2(x) ?
The integral of 12xsec^2(x) is 12(xtan(x)+ln|cos(x)|)+C