What is the integral of 2x^3y^4+x ?

The integral of 2x^3y^4+x is (x^2)/2+(y^4x^4)/2+C

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integral of 2x^3y^4+x

\int 2 x^{3} y^{4} + x d x

\frac{x ^{2}}{2} + \frac{y ^{4} x ^{4}}{2} + C

Solution steps

\int 2 x^{3} y^{4} + x 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 x d x + \int 2 y^{4} x^{3} d x

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

\int 2 y^{4} x^{3} d x = \frac{y ^{4} x ^{4}}{2}

= \frac{x ^{2}}{2} + \frac{y ^{4} x ^{4}}{2}

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{y ^{4} x ^{4}}{2} + C

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What is the integral of 2x^3y^4+x ?
The integral of 2x^3y^4+x is (x^2)/2+(y^4x^4)/2+C