What is the integral of 2ln(x) ?

The integral of 2ln(x) is 2(xln(x)-x)+C

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integral of 2ln(x)

\int 2 ln (x) d x

2 (x ln (x) - x) + C

Solution steps

\int 2 ln (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int ln (x) d x

Apply Integration By Parts

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

= 2 (x ln (x) - \int 1 d x)

\int 1 d x = x

= 2 (x ln (x) - x)

Add a constant to the solution

= 2 (x ln (x) - x) + C

\int (sin (5 x)) d x

\int 9 (tan (x)) (ln (cos (x))) d x

f (x) = 8 x tan (x), at x = π

f (x) = 3 - x

4 y^{^{''}} - 20 y^{^{'}} + 25 y = 0