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Popular >

integral of ln(v)

Solution

\int ln (v) d v

Solution

v ln (v) - v + C

Solution steps

\int ln (v) d v

Apply Integration By Parts

: v ln (v) - \int 1 d v

= v ln (v) - \int 1 d v

\int 1 d v = v

= v ln (v) - v

Add a constant to the solution

= v ln (v) - v + C

Popular Examples

(\partial)/(\partial x)(e^{-x^3})

\frac{\partial}{\partial x} (e^{- x^{3}})

tangent of f(x)= 3/(sqrt(x))tangent of

f (x) = \frac{3}{x}

(\partial)/(\partial y)(6x^{1/3}y^{2/3})

\frac{\partial}{\partial y} (6 x^{\frac{1}{3}} y^{\frac{2}{3}})

(\partial)/(\partial x)((4x)/((y+2z)^3))

\frac{\partial}{\partial x} (\frac{4 x}{( y + 2 z ) ^{3}})

limit as x approaches 0 of 1/x sin(x)

x \to 0 lim (\frac{1}{x} sin (x))

Frequently Asked Questions (FAQ)

What is the integral of ln(v) ?
The integral of ln(v) is vln(v)-v+C