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

The integral of sec^2(2-6x) is 1/6 tan(-2+6x)+C

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integral of sec^2(2-6x)

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

\frac{1}{6} tan (- 2 + 6 x) + C

Solution steps

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

Factor

2 - 6 x : - (- 2 + 6 x)

= \int sec^{2} (- (- 2 + 6 x)) d x

Simplify

sec^{2} (- (- 2 + 6 x)) : sec^{2} (- 2 + 6 x)

= \int sec^{2} (- 2 + 6 x) d x

Apply u-substitution

: \int sec^{2} (u) \frac{1}{6} d u

= \int sec^{2} (u) \frac{1}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int sec^{2} (u) d u

Use the common integral:

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

= \frac{1}{6} tan (u)

Substitute back

u = - 2 + 6 x

= \frac{1}{6} tan (- 2 + 6 x)

Add a constant to the solution

= \frac{1}{6} tan (- 2 + 6 x) + C

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What is the integral of sec^2(2-6x) ?
The integral of sec^2(2-6x) is 1/6 tan(-2+6x)+C