What is the integral of 6xsec^2(2x) ?

The integral of 6xsec^2(2x) is 6(1/2 xtan(2x)+1/4 ln|cos(2x)|)+C

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integral of 6xsec^2(2x)

\int 6 x sec^{2} (2 x) d x

6 (\frac{1}{2} x tan (2 x) + \frac{1}{4} ln ∣ cos (2 x) ∣) + C

Solution steps

\int 6 x sec^{2} (2 x) d x

Take the constant out:

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

= 6 \cdot \int x sec^{2} (2 x) d x

Apply Integration By Parts

: \frac{1}{2} x tan (2 x) - \int \frac{1}{2} tan (2 x) d x

= 6 (\frac{1}{2} x tan (2 x) - \int \frac{1}{2} tan (2 x) d x)

\int \frac{1}{2} tan (2 x) d x = - \frac{1}{4} ln ∣ cos (2 x) ∣

= 6 (\frac{1}{2} x tan (2 x) - (- \frac{1}{4} ln ∣ cos (2 x) ∣))

Simplify

= 6 (\frac{1}{2} x tan (2 x) + \frac{1}{4} ln ∣ cos (2 x) ∣)

Add a constant to the solution

= 6 (\frac{1}{2} x tan (2 x) + \frac{1}{4} ln ∣ cos (2 x) ∣) + C

n = 0 \sum \infty 3 - 7 (0.6)^{n}

\int \frac{1}{1 + e ^{z}} d z

x + y^{2} = 6, x + y = 0

y = (x^{6} - 7 x + 4) (x^{4} - 5 x)

What is the integral of 6xsec^2(2x) ?
The integral of 6xsec^2(2x) is 6(1/2 xtan(2x)+1/4 ln|cos(2x)|)+C