What is the integral of 5xsec^2(x) ?

The integral of 5xsec^2(x) is 5(xtan(x)+ln|cos(x)|)+C

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integral of 5xsec^2(x)

\int 5 x sec^{2} (x) d x

5 (x tan (x) + ln ∣ cos (x) ∣) + C

Solution steps

\int 5 x sec^{2} (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^{2} (x) d x

Apply Integration By Parts

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

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

\int tan (x) d x = - ln ∣ cos (x) ∣

= 5 (x tan (x) - (- ln ∣ cos (x) ∣))

Simplify

= 5 (x tan (x) + ln ∣ cos (x) ∣)

Add a constant to the solution

= 5 (x tan (x) + ln ∣ cos (x) ∣) + C

\int (x^{2} + 2 x) d x

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\int - 3 tan (3 y) d y

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

\frac{\partial}{\partial y} (x^{2} sin^{2} (yz))

What is the integral of 5xsec^2(x) ?
The integral of 5xsec^2(x) is 5(xtan(x)+ln|cos(x)|)+C