What is the integral of y^2z+2xz^3 ?

The integral of y^2z+2xz^3 is y^2zx+z^3x^2+C

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integral of y^2z+2xz^3

\int y^{2} z + 2 x z^{3} d x

y^{2} z x + z^{3} x^{2} + C

Solution steps

\int y^{2} z + 2 x z^{3} 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 y^{2} z d x + \int 2 z^{3} x d x

\int y^{2} z d x = y^{2} z x

\int 2 z^{3} x d x = z^{3} x^{2}

= y^{2} z x + z^{3} x^{2}

Add a constant to the solution

= y^{2} z x + z^{3} x^{2} + C

\frac{d}{d x} (2 (16 e^{4 x} x + 8 e^{4 x}))

\int \frac{3}{x ^{2} - 6 x - 7} d x

- x^{2} + 16, - \frac{1}{4} x - 1, x - 6.6

\frac{d}{d x} (7 x + 5)

y^{'} = y^{3} - 4 y

What is the integral of y^2z+2xz^3 ?
The integral of y^2z+2xz^3 is y^2zx+z^3x^2+C