What is the integral of (sec(x/(14)))^2tan(x/(14)) ?

The integral of (sec(x/(14)))^2tan(x/(14)) is 7tan^2(x/(14))+C

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integral of (sec(x/(14)))^2tan(x/(14))

\int (sec (\frac{x}{14}))^{2} tan (\frac{x}{14}) d x

7 tan^{2} (\frac{x}{14}) + C

Solution steps

\int (sec (\frac{x}{14}))^{2} tan (\frac{x}{14}) d x

Simplify

= \int sec^{2} (\frac{x}{14}) tan (\frac{x}{14}) d x

Apply u-substitution

: \int sec^{2} (u) tan (u) \cdot 14 d u

= \int sec^{2} (u) tan (u) \cdot 14 d u

Take the constant out:

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

= 14 \cdot \int sec^{2} (u) tan (u) d u

Apply u-substitution

: \int v d v

= 14 \cdot \int v d v

Apply the Power Rule

: \frac{v ^{2}}{2}

= 14 \cdot \frac{v ^{2}}{2}

Substitute back

= 14 \cdot \frac{tan ^{2} ( \frac{x}{14} )}{2}

Simplify

14 \cdot \frac{tan ^{2} ( \frac{x}{14} )}{2} : 7 tan^{2} (\frac{x}{14})

= 7 tan^{2} (\frac{x}{14})

Add a constant to the solution

= 7 tan^{2} (\frac{x}{14}) + C

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What is the integral of (sec(x/(14)))^2tan(x/(14)) ?
The integral of (sec(x/(14)))^2tan(x/(14)) is 7tan^2(x/(14))+C