What is the integral of 13xsec^2(x) ?

The integral of 13xsec^2(x) is 13(xtan(x)+ln|cos(x)|)+C

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integral of 13xsec^2(x)

\int 13 x sec^{2} (x) d x

13 (x tan (x) + ln ∣ cos (x) ∣) + C

Solution steps

\int 13 x sec^{2} (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 13 \cdot \int x sec^{2} (x) d x

Apply Integration By Parts

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

= 13 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 13 (x tan (x) - (- ln ∣ cos (x) ∣))

Simplify

= 13 (x tan (x) + ln ∣ cos (x) ∣)

Add a constant to the solution

= 13 (x tan (x) + ln ∣ cos (x) ∣) + C

\int \frac{- x ^{2} + 3 x + 20}{3 x ^{3} + 12 x} d x

\int - sin (2 x) \cdot 2 d x

\int \frac{- 19 x ^{2} + 50 x - 25}{x ^{2} ( 3 x - 5 )} d x

\int \frac{1}{y ^{2} + 1} d y

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

What is the integral of 13xsec^2(x) ?
The integral of 13xsec^2(x) is 13(xtan(x)+ln|cos(x)|)+C