What is the integral of 6xsec(x)tan(x) ?

The integral of 6xsec(x)tan(x) is 6(xsec(x)-ln|tan(x)+sec(x)|)+C

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integral of 6xsec(x)tan(x)

\int 6 x sec (x) tan (x) d x

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

Solution steps

\int 6 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

= 6 \cdot \int x sec (x) tan (x) d x

Apply Integration By Parts

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

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

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

= 6 (x sec (x) - ln ∣ tan (x) + sec (x) ∣)

Add a constant to the solution

= 6 (x sec (x) - ln ∣ tan (x) + sec (x) ∣) + C

\frac{d}{d x} (60 x^{4} - 180 x^{3} + 180 x^{2} - 60 x)

\frac{d}{d x} (ln (x^{2} + 10))

\frac{d}{d t} (10000 (12 + t) e^{- 0.05 t})

\int \frac{5}{( 3 x - 1 )} d x

\frac{d}{d x} (e^{60 x + 50 x^{2}})

What is the integral of 6xsec(x)tan(x) ?
The integral of 6xsec(x)tan(x) is 6(xsec(x)-ln|tan(x)+sec(x)|)+C