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

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

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integral of 6sec(x)tan(x)

\int 6 sec (x) tan (x) d x

6 sec (x) + C

Solution steps

\int 6 sec (x) tan (x) d x

Take the constant out:

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

= 6 \cdot \int sec (x) tan (x) d x

Apply u-substitution

= 6 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 6 \cdot 1 \cdot u

Substitute back

u = sec (x)

= 6 \cdot 1 \cdot sec (x)

Simplify

= 6 sec (x)

Add a constant to the solution

= 6 sec (x) + C

\frac{d}{d x} ((x^{2} - 3)^{5})

\int \frac{2 x}{- x ^{2} - 1} d x

\int \frac{( 2 x ^{4} + 2 5 x )}{x} d x

t \to 0 lim (\frac{( 2 + t ) ^{3} - 8}{t})

x \to - 2 lim (4 x + 1)

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