What is the integral of 6/7 sec^2(x/7) ?

The integral of 6/7 sec^2(x/7) is 6tan(x/7)+C

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integral of 6/7 sec^2(x/7)

\int \frac{6}{7} sec^{2} (\frac{x}{7}) d x

6 tan (\frac{x}{7}) + C

Solution steps

\int \frac{6}{7} sec^{2} (\frac{x}{7}) d x

Take the constant out:

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

= \frac{6}{7} \cdot \int sec^{2} (\frac{x}{7}) d x

Apply u-substitution

= \frac{6}{7} \cdot \int sec^{2} (u) \cdot 7 d u

Take the constant out:

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

= \frac{6}{7} \cdot 7 \cdot \int sec^{2} (u) d u

Use the common integral:

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

= \frac{6}{7} \cdot 7 tan (u)

Substitute back

u = \frac{x}{7}

= \frac{6}{7} \cdot 7 tan (\frac{x}{7})

Simplify

\frac{6}{7} \cdot 7 tan (\frac{x}{7}) : 6 tan (\frac{x}{7})

= 6 tan (\frac{x}{7})

Add a constant to the solution

= 6 tan (\frac{x}{7}) + C

What is the integral of 6/7 sec^2(x/7) ?
The integral of 6/7 sec^2(x/7) is 6tan(x/7)+C