What is the integral of 12sec^2(6x)tan(6x) ?

The integral of 12sec^2(6x)tan(6x) is tan^2(6x)+C

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integral of 12sec^2(6x)tan(6x)

\int 12 sec^{2} (6 x) tan (6 x) d x

tan^{2} (6 x) + C

Solution steps

\int 12 sec^{2} (6 x) tan (6 x) d x

Take the constant out:

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

= 12 \cdot \int sec^{2} (6 x) tan (6 x) d x

Apply u-substitution

: \int \frac{u}{6} d u

= 12 \cdot \int \frac{u}{6} d u

Take the constant out:

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

= 12 \cdot \frac{1}{6} \cdot \int u d u

Apply the Power Rule

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

= 12 \cdot \frac{1}{6} \cdot \frac{u ^{2}}{2}

Substitute back

u = tan (6 x)

= 12 \cdot \frac{1}{6} \cdot \frac{tan ^{2} ( 6 x )}{2}

Simplify

12 \cdot \frac{1}{6} \cdot \frac{tan ^{2} ( 6 x )}{2} : tan^{2} (6 x)

= tan^{2} (6 x)

Add a constant to the solution

= tan^{2} (6 x) + C

\int \frac{1}{( x + 1 ) ( x + 5 )} d x

\int tan^{3} (9 x) sec (9 x) d x

y = cos (a^{9} + x^{9})

y = 6 x^{2} - 3 x, at 1, 5

(8.1) (4.1)

What is the integral of 12sec^2(6x)tan(6x) ?
The integral of 12sec^2(6x)tan(6x) is tan^2(6x)+C