What is the integral of 1.3yln(x^{1.3}y^2)-1.3y ?

The integral of 1.3yln(x^{1.3}y^2)-1.3y is -2.99yx+1.69yxln(x)+2.6yxln(y)+C

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integral of 1.3yln(x^{1.3}y^2)-1.3y

\int 1.3 y ln (x^{1.3} y^{2}) - 1.3 y d x

- 2.99 y x + 1.69 y x ln (x) + 2.6 y x ln (y) + C

Solution steps

\int 1.3 y ln (x^{1.3} y^{2}) - 1.3 y d x

1.3 ln (y^{2} x^{1.3}) y = 1.3 y (1.3 ln (x) + 2 ln (y))

= \int - 1.3 y + 1.3 y (1.3 ln (x) + 2 ln (y)) 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 1.3 y d x + \int 1.3 y (1.3 ln (x) + 2 ln (y)) d x

\int 1.3 y d x = 1.3 y x

\int 1.3 y (1.3 ln (x) + 2 ln (y)) d x = 1.3 y (1.3 (x ln (x) - x) + 2 ln (y) x)

= - 1.3 y x + 1.3 y (1.3 (x ln (x) - x) + 2 ln (y) x)

Simplify

- 1.3 y x + 1.3 y (1.3 (x ln (x) - x) + 2 ln (y) x) : - 2.99 y x + 1.69 y x ln (x) + 2.6 y x ln (y)

= - 2.99 y x + 1.69 y x ln (x) + 2.6 y x ln (y)

Add a constant to the solution

= - 2.99 y x + 1.69 y x ln (x) + 2.6 y x ln (y) + C

\frac{d}{d x} (3 x + 2 y)

x \to 3 lim (\frac{9 - x ^{2}}{x - 3})

y = sin (7 x) + cos (2 x)

y = (x)^{3 x}

\frac{d}{d x} (x e^{- x} + e^{3 x})

What is the integral of 1.3yln(x^{1.3}y^2)-1.3y ?
The integral of 1.3yln(x^{1.3}y^2)-1.3y is -2.99yx+1.69yxln(x)+2.6yxln(y)+C