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Popular >

integral of y/x+6x

Solution

\int \frac{y}{x} + 6 x d x

Solution

y ln ∣ x ∣ + 3 x^{2} + C

Solution steps

\int \frac{y}{x} + 6 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{y}{x} d x + \int 6 x d x

\int \frac{y}{x} d x = y ln ∣ x ∣

\int 6 x d x = 3 x^{2}

= y ln ∣ x ∣ + 3 x^{2}

Add a constant to the solution

= y ln ∣ x ∣ + 3 x^{2} + C

Popular Examples

derivative of 1/x y

\frac{d}{d x} (\frac{1}{x} y)

derivative of 2e^x+4/(\sqrt[3]{x})

limit as x approaches-3+of (4x+3)/(x+3)

x \to - 3 + lim (\frac{4 x + 3}{x + 3})

(dy)/(dx)=2xy^{1/2}

\frac{d y}{d x} = 2 x y^{\frac{1}{2}}

area 4-x^2,16-7x area

4 - x^{2}, 16 - 7 x

Frequently Asked Questions (FAQ)

What is the integral of y/x+6x ?
The integral of y/x+6x is yln|x|+3x^2+C