What is the integral of 8xsec(x)tan(x) ?

The integral of 8xsec(x)tan(x) is 8(xsec(x)-ln|tan(x)+sec(x)|)+C

integral of 8xsec(x)tan(x)

\int 8 x sec (x) tan (x) d x

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

Solution steps

\int 8 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

= 8 \cdot \int x sec (x) tan (x) d x

Apply Integration By Parts

= 8 (x sec (x) - \int sec (x) d x)

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

= 8 (x sec (x) - ln ∣ tan (x) + sec (x) ∣)

Add a constant to the solution

= 8 (x sec (x) - ln ∣ tan (x) + sec (x) ∣) + C

\frac{\partial}{\partial x} (x y (- 3 - x - y))

\int 3 sec (2) (x) + 2 x - 8 x d x

\frac{\partial}{\partial x} (ln (7 x^{2} + x y))

y^{^{''}} + 3 y^{^{'}} + 2 y = cos (e x)

\int \frac{9 x ^{2}}{2} - 5 cos (x) + 7 d x

What is the integral of 8xsec(x)tan(x) ?
The integral of 8xsec(x)tan(x) is 8(xsec(x)-ln|tan(x)+sec(x)|)+C