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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

Graph

Popular Examples

integral from 0 to pi/2 of 10cos^5(x)

\int_{0}^{\frac{π}{2}} 10 cos^{5} (x) d x

integral of 3x^{4/3}-sin(x)+c

\int 3 x^{\frac{4}{3}} - sin (x) + c d x

derivative of (e^{3x}/(x^6))

\frac{d}{d x} (\frac{e ^{3 x}}{x ^{6}})

integral of 1/((x+2)(x+3))

\int \frac{1}{( x + 2 ) ( x + 3 )} d x

integral of (5x^2+3x-2)/(x^3+2x^2)

\int \frac{5 x ^{2} + 3 x - 2}{x ^{3} + 2 x ^{2}} d 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