What is the integral of (1-5/y+x) ?

The integral of (1-5/y+x) is y-5ln|y|+xy+C

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integral of (1-5/y+x)

\int (1 - \frac{5}{y} + x) d y

y - 5 ln ∣ y ∣ + x y + C

Solution steps

\int 1 - \frac{5}{y} + x d y

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 y - \int \frac{5}{y} d y + \int x d y

\int 1 d y = y

\int \frac{5}{y} d y = 5 ln ∣ y ∣

\int x d y = x y

= y - 5 ln ∣ y ∣ + x y

Add a constant to the solution

= y - 5 ln ∣ y ∣ + x y + C

y = (4 e)^{x}

\frac{d}{d x} (\frac{1 - 5 x ^{2}}{3 3 + 2 x})

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

f (x) = (2 x + 7)^{2}

- 16 t^{2}