What is the integral of sec^2(x/3) ?

The integral of sec^2(x/3) is 3tan(x/3)+C

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integral of sec^2(x/3)

\int sec^{2} (\frac{x}{3}) d x

3 tan (\frac{x}{3}) + C

Solution steps

\int sec^{2} (\frac{x}{3}) d x

Apply u-substitution

: \int sec^{2} (u) \cdot 3 d u

= \int sec^{2} (u) \cdot 3 d u

Take the constant out:

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

= 3 \cdot \int sec^{2} (u) d u

Use the common integral:

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

= 3 tan (u)

Substitute back

u = \frac{x}{3}

= 3 tan (\frac{x}{3})

Add a constant to the solution

= 3 tan (\frac{x}{3}) + C

\frac{\partial}{\partial x} (ln (4 x))

y = 5 x^{2} - 10 x - 6 x^{- 2}

\frac{d}{d x} (\frac{sin ( x )}{cos ( x )})

\frac{\partial}{\partial x} (- \frac{x - y}{x ^{2} ( x + y )})

f (x) = 2 (13 - x^{4})