What is the integral of 7ln(x) ?

The integral of 7ln(x) is 7(xln(x)-x)+C

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integral of 7ln(x)

\int 7 ln (x) d x

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

Solution steps

\int 7 ln (x) d x

Take the constant out:

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

= 7 \cdot \int ln (x) d x

Apply Integration By Parts

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

= 7 (x ln (x) - \int 1 d x)

\int 1 d x = x

= 7 (x ln (x) - x)

Add a constant to the solution

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

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

\frac{d}{d x} ((x - 1)^{\frac{2}{3}})

(x^{2} + y^{2}) d x + (2 x y) d y = 0

y^{^{'}} = \frac{x ^{2} - y ^{2}}{x y}, y (2) = 5