What is the integral of 3xzy+xy^2+2zx^2 ?

The integral of 3xzy+xy^2+2zx^2 is (y^2x^2)/2+(2zx^3)/3+(3zyx^2)/2+C

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integral of 3xzy+xy^2+2zx^2

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

\frac{y ^{2} x ^{2}}{2} + \frac{2 z x ^{3}}{3} + \frac{3 zy x ^{2}}{2} + C

Solution steps

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

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

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

\int 3 zy x d x = \frac{3 zy x ^{2}}{2}

= \frac{y ^{2} x ^{2}}{2} + \frac{2 z x ^{3}}{3} + \frac{3 zy x ^{2}}{2}

Add a constant to the solution

= \frac{y ^{2} x ^{2}}{2} + \frac{2 z x ^{3}}{3} + \frac{3 zy x ^{2}}{2} + C

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

\int \frac{( x ^{2} + 4 )}{( x - 5 ) ( x ^{2} + 9 )} d x

\int x^{4} e^{(1 - x^{5})} d x

\frac{d y}{d x} + 5 y = 8

\frac{d}{d x} (sin (x^{2} + sin (x^{2} + sin (x^{2}))))

What is the integral of 3xzy+xy^2+2zx^2 ?
The integral of 3xzy+xy^2+2zx^2 is (y^2x^2)/2+(2zx^3)/3+(3zyx^2)/2+C