What is the integral of 7x+14xln(3x) ?

The integral of 7x+14xln(3x) is 7x^2ln(3x)+C

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integral of 7x+14xln(3x)

\int 7 x + 14 x ln (3 x) d x

7 x^{2} ln (3 x) + C

Solution steps

\int 7 x + 14 x ln (3 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 7 x d x + \int 14 x ln (3 x) d x

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 14 x ln (3 x) d x = 14 (\frac{1}{2} x^{2} ln (3 x) - \frac{x ^{2}}{4})

= \frac{7 x ^{2}}{2} + 14 (\frac{1}{2} x^{2} ln (3 x) - \frac{x ^{2}}{4})

Simplify

\frac{7 x ^{2}}{2} + 14 (\frac{1}{2} x^{2} ln (3 x) - \frac{x ^{2}}{4}) : 7 x^{2} ln (3 x)

= 7 x^{2} ln (3 x)

Add a constant to the solution

= 7 x^{2} ln (3 x) + C

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What is the integral of 7x+14xln(3x) ?
The integral of 7x+14xln(3x) is 7x^2ln(3x)+C