What is the integral of 4xsec^2(x) ?

The integral of 4xsec^2(x) is 4(xtan(x)+ln|cos(x)|)+C

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integral of 4xsec^2(x)

\int 4 x sec^{2} (x) d x

4 (x tan (x) + ln ∣ cos (x) ∣) + C

Solution steps

\int 4 x sec^{2} (x) d x

Take the constant out:

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

= 4 \cdot \int x sec^{2} (x) d x

Apply Integration By Parts

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

= 4 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 4 (x tan (x) - (- ln ∣ cos (x) ∣))

Simplify

= 4 (x tan (x) + ln ∣ cos (x) ∣)

Add a constant to the solution

= 4 (x tan (x) + ln ∣ cos (x) ∣) + C

\frac{d}{d x} (0.2 x)

\int tan (x) sin (x) d x

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

x + 2, \frac{1}{x + 1}, x = 2, x = 0

6 e^{x} + \frac{2}{3 x}

What is the integral of 4xsec^2(x) ?
The integral of 4xsec^2(x) is 4(xtan(x)+ln|cos(x)|)+C