What is the integral of 1/(cos^2(2y)) ?

The integral of 1/(cos^2(2y)) is 1/2 tan(2y)+C

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integral of 1/(cos^2(2y))

\int \frac{1}{cos ^{2} ( 2 y )} d y

\frac{1}{2} tan (2 y) + C

Solution steps

\int \frac{1}{cos ^{2} ( 2 y )} d y

Rewrite using trig identities

= \int sec^{2} (2 y) d y

Apply u-substitution

: \int sec^{2} (u) \frac{1}{2} d u

= \int sec^{2} (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= \frac{1}{2} tan (u)

Substitute back

u = 2 y

= \frac{1}{2} tan (2 y)

Add a constant to the solution

= \frac{1}{2} tan (2 y) + C

f (x) = 14 (2 x + 5)^{6}

\frac{\partial}{\partial y} (\frac{y ^{3}}{x})

t^{8} cos (t)

t^{2} \cdot e^{-, at}

f (x) = x (4 - x)^{3}, at x = 2

What is the integral of 1/(cos^2(2y)) ?
The integral of 1/(cos^2(2y)) is 1/2 tan(2y)+C