What is the integral of 3xsec(x)tan(x) ?

The integral of 3xsec(x)tan(x) is 3(xsec(x)-ln|tan(x)+sec(x)|)+C

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integral of 3xsec(x)tan(x)

\int 3 x sec (x) tan (x) d x

3 (x sec (x) - ln ∣ tan (x) + sec (x) ∣) + C

Solution steps

\int 3 x sec (x) tan (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 (x) tan (x) d x

Apply Integration By Parts

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

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

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= 3 (x sec (x) - ln ∣ tan (x) + sec (x) ∣)

Add a constant to the solution

= 3 (x sec (x) - ln ∣ tan (x) + sec (x) ∣) + C

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

\int x e^{- 4 x^{2}} d x

f (x) = (sin (x))^{x}

\int e^{2 x} d x

\frac{\partial}{\partial y} (\frac{x ^{2}}{4 y ^{4}})

What is the integral of 3xsec(x)tan(x) ?
The integral of 3xsec(x)tan(x) is 3(xsec(x)-ln|tan(x)+sec(x)|)+C