What is the integral of 20tan(2x)sec^2(2x) ?

The integral of 20tan(2x)sec^2(2x) is 5tan^2(2x)+C

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integral of 20tan(2x)sec^2(2x)

\int 20 tan (2 x) sec^{2} (2 x) d x

5 tan^{2} (2 x) + C

Solution steps

\int 20 tan (2 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

= 20 \cdot \int tan (2 x) sec^{2} (2 x) d x

Apply u-substitution

: \int \frac{u}{2} d u

= 20 \cdot \int \frac{u}{2} d u

Take the constant out:

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

= 20 \cdot \frac{1}{2} \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= 20 \cdot \frac{1}{2} \cdot \frac{u ^{2}}{2}

Substitute back

u = tan (2 x)

= 20 \cdot \frac{1}{2} \cdot \frac{tan ^{2} ( 2 x )}{2}

Simplify

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

= 5 tan^{2} (2 x)

Add a constant to the solution

= 5 tan^{2} (2 x) + C

\frac{d}{d x} (sin (ln (4 x)))

e^{- 4 x^{2}}

x \to - 1 lim (16 - 4 x)

\int ((y) ln (1 + y)) d y

\int (2 + \frac{5}{7} x - 6 x^{2}) d x

What is the integral of 20tan(2x)sec^2(2x) ?
The integral of 20tan(2x)sec^2(2x) is 5tan^2(2x)+C