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Popular >

integral of ln(x)+x

Solution

\int ln (x) + x d x

Solution

x ln (x) - x + \frac{x ^{2}}{2} + C

Solution steps

\int ln (x) + 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 ln (x) d x + \int x d x

\int ln (x) d x = x ln (x) - x

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

= x ln (x) - x + \frac{x ^{2}}{2}

Add a constant to the solution

= x ln (x) - x + \frac{x ^{2}}{2} + C

Popular Examples

integral of sin^3(18x)

\int sin^{3} (18 x) d x

integral of sec^{4x}(x

\int sec^{4 x} (d) x d x

derivative of (x^2-64/(x+8))

\frac{d}{d x} (\frac{x ^{2} - 64}{x + 8})

derivative of g(t)=(9t+5)^2(5t-6)^{-3}derivative of

g (t) = (9 t + 5)^{2} (5 t - 6)^{- 3}

(3x+2)+(3y-3)y^'=0

(3 x + 2) + (3 y - 3) y^{^{'}} = 0

Frequently Asked Questions (FAQ)

What is the integral of ln(x)+x ?
The integral of ln(x)+x is xln(x)-x+(x^2)/2+C