What is the integral of 8xsec^2(x) ?

The integral of 8xsec^2(x) is 8(xtan(x)+ln|cos(x)|)+C

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integral of 8xsec^2(x)

\int 8 x sec^{2} (x) d x

8 (x tan (x) + ln ∣ cos (x) ∣) + C

Solution steps

\int 8 x sec^{2} (x) d x

Take the constant out:

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

= 8 \cdot \int x sec^{2} (x) d x

Apply Integration By Parts

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

= 8 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 8 (x tan (x) - (- ln ∣ cos (x) ∣))

Simplify

= 8 (x tan (x) + ln ∣ cos (x) ∣)

Add a constant to the solution

= 8 (x tan (x) + ln ∣ cos (x) ∣) + C

\int x sin (2 a x) d x

y = (1 + 6 x^{2}) (x - x^{2})

n = 1 \sum \infty \frac{5}{n ^{4}}

x \to \infty lim (\frac{x}{3 x})

\frac{d ^{2}}{d x ^{2}} (\frac{1}{4 x ^{2} + 5 x})

What is the integral of 8xsec^2(x) ?
The integral of 8xsec^2(x) is 8(xtan(x)+ln|cos(x)|)+C