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Popular >

integral of 5x+y

Solution

\int 5 x + y d y

Solution

\frac{y ^{2}}{2} + 5 x y + C

Solution steps

\int 5 x + y d y

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 y + \int 5 x d y

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

\int 5 x d y = 5 x y

= \frac{y ^{2}}{2} + 5 x y

Add a constant to the solution

= \frac{y ^{2}}{2} + 5 x y + C

Popular Examples

derivative of-sqrt(2x)

\frac{d}{d x} (- 2 x)

integral of sqrt(1+3sin^2(x))

\int 1 + 3 sin^{2} (x) d x

integral of (esqrt(x))/(sqrt(x))

\int \frac{e x}{x} d x

integral of (sec(x))^6

\int (sec (x))^{6} d x

limit as x approaches 0+of (-5+x)/(4+x)

x \to 0 + lim (\frac{- 5 + x}{4 + x})

Frequently Asked Questions (FAQ)

What is the integral of 5x+y ?
The integral of 5x+y is (y^2)/2+5xy+C