What is the integral of 5sec^2(2x) ?

The integral of 5sec^2(2x) is 5/2 tan(2x)+C

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integral of 5sec^2(2x)

\int 5 sec^{2} (2 x) d x

\frac{5}{2} tan (2 x) + C

Solution steps

\int 5 sec^{2} (2 x) d x

Take the constant out:

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

= 5 \cdot \int sec^{2} (2 x) d x

Apply u-substitution

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

= 5 \cdot \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

= 5 \cdot \frac{1}{2} \cdot \int sec^{2} (u) d u

Use the common integral:

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

= 5 \cdot \frac{1}{2} tan (u)

Substitute back

u = 2 x

= 5 \cdot \frac{1}{2} tan (2 x)

Simplify

5 \cdot \frac{1}{2} tan (2 x) : \frac{5}{2} tan (2 x)

= \frac{5}{2} tan (2 x)

Add a constant to the solution

= \frac{5}{2} tan (2 x) + C

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What is the integral of 5sec^2(2x) ?
The integral of 5sec^2(2x) is 5/2 tan(2x)+C