What is the integral of 4t^3y-15t^2-y ?

The integral of 4t^3y-15t^2-y is -yt-5t^3+yt^4+C

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integral of 4t^3y-15t^2-y

\int 4 t^{3} y - 15 t^{2} - y d t

- y t - 5 t^{3} + y t^{4} + C

Solution steps

\int 4 t^{3} y - 15 t^{2} - y d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int y d t - \int 15 t^{2} d t + \int 4 y t^{3} d t

\int y d t = y t

\int 15 t^{2} d t = 5 t^{3}

\int 4 y t^{3} d t = y t^{4}

= - y t - 5 t^{3} + y t^{4}

Add a constant to the solution

= - y t - 5 t^{3} + y t^{4} + C

11 x - 3, 10 x - 5, [12, 34]

\int \frac{1}{t ^{2} + 1} d t

x \to 129 lim (\frac{x - 129}{x + 15 - 12})

\frac{d}{d x} (3^{a r c t a n (x)})

\frac{\partial}{\partial x} (x y^{2} - 2 y^{3} + 3 x z)

What is the integral of 4t^3y-15t^2-y ?
The integral of 4t^3y-15t^2-y is -yt-5t^3+yt^4+C