What is the integral of (2ysin(x)-x^3+ln(y)) ?

The integral of (2ysin(x)-x^3+ln(y)) is yln(y)-y-x^3y+y^2sin(x)+C

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integral of (2ysin(x)-x^3+ln(y))

\int (2 y sin (x) - x^{3} + ln (y)) d y

y ln (y) - y - x^{3} y + y^{2} sin (x) + C

Solution steps

\int 2 y sin (x) - x^{3} + ln (y) 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 ln (y) d y - \int x^{3} d y + \int 2 sin (x) y d y

\int ln (y) d y = y ln (y) - y

\int x^{3} d y = x^{3} y

\int 2 sin (x) y d y = y^{2} sin (x)

= y ln (y) - y - x^{3} y + y^{2} sin (x)

Add a constant to the solution

= y ln (y) - y - x^{3} y + y^{2} sin (x) + C

y^{^{''}} - 9 y^{^{'}} = 81 t

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\frac{( 6 x - 7 ) ^{2}}{x ^{4}}

\frac{d}{d x} (tan (x) + \frac{1}{x ^{2}})

\int 4 - x d x

What is the integral of (2ysin(x)-x^3+ln(y)) ?
The integral of (2ysin(x)-x^3+ln(y)) is yln(y)-y-x^3y+y^2sin(x)+C