What is the integral of 5xsec(x)tan(x) ?

The integral of 5xsec(x)tan(x) is 5(xsec(x)-ln|tan(x)+sec(x)|)+C

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integral of 5xsec(x)tan(x)

\int 5 x sec (x) tan (x) d x

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

Solution steps

\int 5 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

= 5 \cdot \int x sec (x) tan (x) d x

Apply Integration By Parts

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

= 5 (x sec (x) - \int sec (x) d x)

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

= 5 (x sec (x) - ln ∣ tan (x) + sec (x) ∣)

Add a constant to the solution

= 5 (x sec (x) - ln ∣ tan (x) + sec (x) ∣) + C

\frac{d}{d y} (x - y)

\frac{2}{s + 1} + \frac{24 s}{s ^{2} + 9}

f^{^{''}} (x) = 4, f^{^{'}} (2) = 10, f (2) = 15

\frac{\partial}{\partial x} (r t)

x^{2} + x y + 2 y^{2} = 8, (- 2, - 1)

What is the integral of 5xsec(x)tan(x) ?
The integral of 5xsec(x)tan(x) is 5(xsec(x)-ln|tan(x)+sec(x)|)+C