What is the integral of 3xsec^2(x) ?

The integral of 3xsec^2(x) is 3(xtan(x)+ln|cos(x)|)+C

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integral of 3xsec^2(x)

\int 3 x sec^{2} (x) d x

3 (x tan (x) + ln ∣ cos (x) ∣) + C

Solution steps

\int 3 x sec^{2} (x) d x

Take the constant out:

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

= 3 \cdot \int x sec^{2} (x) d x

Apply Integration By Parts

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

= 3 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 3 (x tan (x) - (- ln ∣ cos (x) ∣))

Simplify

= 3 (x tan (x) + ln ∣ cos (x) ∣)

Add a constant to the solution

= 3 (x tan (x) + ln ∣ cos (x) ∣) + C

\int \frac{sin ^{2} ( x )}{cos ^{6} ( x )} d x

\int x lo g_{10} (x) d x

x \to \frac{π}{4} lim (sin (x))

f (x) = \frac{x}{3 x + 4 ln ( x )}

\frac{d y}{d x}, y^{2} = 4 x

What is the integral of 3xsec^2(x) ?
The integral of 3xsec^2(x) is 3(xtan(x)+ln|cos(x)|)+C