What is the integral of $ln (7 x)$ $ln(7x)$ ?

Question

20573 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-12-09T01:01:21

$\int u d v = u v - \int v d u$ $int u dv=uv- int v du$

Let $u = ln (7 x)$ $u=ln(7x)" "$ $d v = d x$ $" "dv=dx$
$\Rightarrow d u = \frac{d x}{x}$ $=> du={dx}/x" "$ $\Rightarrow v = x$ $" "=> v=x$

By Integration by Parts,

$\int ln (7 x) d x = ln (7 x) \cdot x - \int x \cdot \frac{d x}{x}$ $int ln(7x) dx=ln(7x) cdot x- int x cdot {dx}/x$

$= x ln (7 x) - \int d x + C$ $=x ln(7x)-int dx+C$

$= x ln (7 x) - x + C$ $=x ln(7x) - x+C$

I hope that this was helpful.

What is the integral of ln(7x)ln(7x)?