What is the integral of 6xsec^2(x) ?

The integral of 6xsec^2(x) is 6(xtan(x)+ln|cos(x)|)+C

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integral of 6xsec^2(x)

\int 6 x sec^{2} (x) d x

6 (x tan (x) + ln ∣ cos (x) ∣) + C

Solution steps

\int 6 x sec^{2} (x) d x

Take the constant out:

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

= 6 \cdot \int x sec^{2} (x) d x

Apply Integration By Parts

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

= 6 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 6 (x tan (x) - (- ln ∣ cos (x) ∣))

Simplify

= 6 (x tan (x) + ln ∣ cos (x) ∣)

Add a constant to the solution

= 6 (x tan (x) + ln ∣ cos (x) ∣) + C

x y + 2 x \frac{d y}{d x} = y

x \to 0 + lim (\frac{1}{x} - ln (x))

n = 0 \sum \infty (\frac{x + 9}{2})^{n}

x \to 0 lim (\frac{x ^{2}}{3 x})

\frac{\partial}{\partial r} (r ln (r s^{2} t^{3}))

What is the integral of 6xsec^2(x) ?
The integral of 6xsec^2(x) is 6(xtan(x)+ln|cos(x)|)+C