What is the integral of (v(x))/(cos(x)) ?

The integral of (v(x))/(cos(x)) is x/2 v^2sec(x)+C

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integral of (v(x))/(cos(x))

\int \frac{v ( x )}{cos ( x )}

\frac{x}{2} v^{2} sec (x) + C

Solution steps

\int \frac{vx}{cos ( x )} d v

Take the constant out:

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

= \frac{x}{cos ( x )} \cdot \int v d v

Apply the Power Rule

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

= \frac{x}{cos ( x )} \cdot \frac{v ^{2}}{2}

Simplify

\frac{x}{cos ( x )} \cdot \frac{v ^{2}}{2} : \frac{x}{2} v^{2} sec (x)

= \frac{x}{2} v^{2} sec (x)

Add a constant to the solution

= \frac{x}{2} v^{2} sec (x) + C

x \to 2 lim (x^{5} - 32 x)

2 (x^{2} + y^{2}) d x + (7 x y) d y = 0

\int_{0}^{2} \frac{x ^{2}}{x ^{2} + 4} d x

\int (2 - 3 x)^{2} d x

y d x = (y e^{y - 2 x}) d y

What is the integral of (v(x))/(cos(x)) ?
The integral of (v(x))/(cos(x)) is x/2 v^2sec(x)+C