What is the integral of integral of (x^3y+cos(x)) ?

The integral of integral of (x^3y+cos(x)) is Cy+(x^4y^2)/8+sin(x)y+C

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integral of integral of (x^3y+cos(x))

\int \int (x^{3} y + cos (x)) d x d y

C y + \frac{x ^{4} y ^{2}}{8} + sin (x) y + C

Solution steps

\int \int (x^{3} y + cos (x)) d x d y

\int (x^{3} y + cos (x)) d x = sin (x) + \frac{y x ^{4}}{4} + C

= \int (sin (x) + \frac{y x ^{4}}{4} + C) d y

\int (sin (x) + \frac{y x ^{4}}{4} + C) d y = C y + \frac{x ^{4} y ^{2}}{8} + sin (x) y + C

= C y + \frac{x ^{4} y ^{2}}{8} + sin (x) y + C

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What is the integral of integral of (x^3y+cos(x)) ?
The integral of integral of (x^3y+cos(x)) is Cy+(x^4y^2)/8+sin(x)y+C