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Popular >

integral of (y/x+1)

Solution

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

Solution

x + y ln ∣ x ∣ + C

Solution steps

\int \frac{y}{x} + 1 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 1 d x + \int \frac{y}{x} d x

\int 1 d x = x

\int \frac{y}{x} d x = y ln ∣ x ∣

= x + y ln ∣ x ∣

Add a constant to the solution

= x + y ln ∣ x ∣ + C

Popular Examples

integral of-40cos(5y+4)

\int - 40 cos (5 y + 4) d y

integral of (p(x))/((x-2)(x^2+9))

\int \frac{p ( x )}{( x - 2 ) ( x ^{2} + 9 )} d x

integral of 50-8x-26

\int 50 - 8 x - 26 d x

integral of ((sqrt(x^2-1)))/x

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

integral of x^2(x^2+6)^{(-1)/2}

\int x^{2} (x^{2} + 6)^{\frac{- 1}{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of (y/x+1) ?
The integral of (y/x+1) is x+yln|x|+C