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

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

Popular >

integral of xsec^2(2x)

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

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

Solution steps

\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

= \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) ∣

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

Simplify

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

Add a constant to the solution

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

\frac{3}{( s - 1 ) ^{2}}

\int \frac{48 x ^{2}}{( x - 15 ) ( x + 5 ) ^{2}} d x

x \to - 3 lim (4 x^{2} + 3 x + 2)

(1 - x^{2}) \frac{d y}{d x} = x y + y

y = \frac{2 x + 1}{x}

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