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Popular >

integral of (y-x^3)

Solution

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

Solution

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

Solution steps

\int y - x^{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 d x - \int x^{3} d x

\int y d x = y x

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

= y x - \frac{x ^{4}}{4}

Add a constant to the solution

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

Popular Examples

integral of (5x-4)/(sqrt(8x-5^2+9))

\int \frac{5 x - 4}{8 x - 5 ^{2} + 9} d x

(dy)/(dx)+y^9x+4y=0

\frac{d y}{d x} + y^{9} x + 4 y = 0

integral from 0 to 2 of sqrt(4x+1)

\int_{0}^{2} 4 x + 1 d x

limit as x approaches 0 of (ln(6x+1))/x

x \to 0 lim (\frac{ln ( 6 x + 1 )}{x})

integral of r/(sqrt(4-r^2))

\int \frac{r}{4 - r ^{2}} d r

Frequently Asked Questions (FAQ)

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