What is the integral of 4x^3-xy+cos(y) ?

The integral of 4x^3-xy+cos(y) is cos(y)x+x^4-(yx^2)/2+C

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integral of 4x^3-xy+cos(y)

\int 4 x^{3} - x y + cos (y) d x

cos (y) x + x^{4} - \frac{y x ^{2}}{2} + C

Solution steps

\int 4 x^{3} - x y + cos (y) 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 cos (y) d x + \int 4 x^{3} d x - \int y x d x

\int cos (y) d x = cos (y) x

\int 4 x^{3} d x = x^{4}

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

= cos (y) x + x^{4} - \frac{y x ^{2}}{2}

Add a constant to the solution

= cos (y) x + x^{4} - \frac{y x ^{2}}{2} + C

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