What is the integral of 6xsec(3x^2)tan(3x^2) ?

The integral of 6xsec(3x^2)tan(3x^2) is sec(3x^2)+C

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integral of 6xsec(3x^2)tan(3x^2)

\int 6 x sec (3 x^{2}) tan (3 x^{2}) d x

sec (3 x^{2}) + C

Solution steps

\int 6 x sec (3 x^{2}) tan (3 x^{2}) d x

Take the constant out:

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

= 6 \cdot \int x sec (3 x^{2}) tan (3 x^{2}) d x

Apply u-substitution

: \int \frac{sec ( u ) tan ( u )}{6} d u

= 6 \cdot \int \frac{sec ( u ) tan ( u )}{6} d u

Take the constant out:

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

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

Apply u-substitution

: \int 1 d v

= 6 \cdot \frac{1}{6} \cdot \int 1 d v

Integral of a constant:

\int a d x = a x

= 6 \cdot \frac{1}{6} \cdot 1 \cdot v

Substitute back

= 6 \cdot \frac{1}{6} \cdot 1 \cdot sec (3 x^{2})

Simplify

6 \cdot \frac{1}{6} \cdot 1 \cdot sec (3 x^{2}) : sec (3 x^{2})

= sec (3 x^{2})

Add a constant to the solution

= sec (3 x^{2}) + C

x^{2} y^{^{''}} + x y^{^{'}} + 25 y = 0

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

\int_{- 1}^{1} sec^{3} (x) d x

f (x) = \frac{( 2 x + 1 )}{x + 2}, at x = 1

y = \frac{3 x - 4}{2 x + 3}

What is the integral of 6xsec(3x^2)tan(3x^2) ?
The integral of 6xsec(3x^2)tan(3x^2) is sec(3x^2)+C