What is the integral of 7xsec^2(x) ?

The integral of 7xsec^2(x) is 7(xtan(x)+ln|cos(x)|)+C

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integral of 7xsec^2(x)

\int 7 x sec^{2} (x) d x

7 (x tan (x) + ln ∣ cos (x) ∣) + C

Solution steps

\int 7 x sec^{2} (x) d x

Take the constant out:

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

= 7 \cdot \int x sec^{2} (x) d x

Apply Integration By Parts

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

= 7 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 7 (x tan (x) - (- ln ∣ cos (x) ∣))

Simplify

= 7 (x tan (x) + ln ∣ cos (x) ∣)

Add a constant to the solution

= 7 (x tan (x) + ln ∣ cos (x) ∣) + C

\int (2 x y) d x

\int 2 e^{- x^{2}} - 1 d x

\frac{\partial}{\partial z} (x^{\frac{y}{z}})

f (x) = 2 x^{3} \cdot ln (7 x)

\frac{d}{d x} (\frac{4 x ^{2} + 3}{2 x - 1})

What is the integral of 7xsec^2(x) ?
The integral of 7xsec^2(x) is 7(xtan(x)+ln|cos(x)|)+C