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

\int 5 x (x^{2} + 1) d x

\int 2 e^{2 e^{x} + x} d x

\int \frac{2}{( x ^{2} + 4 )} d x

\int (4 - 18 x) d x

\int \frac{1}{4 x + 9} d x

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