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Popular >

integral of ln(6x^4)

Solution

\int ln (6 x^{4}) d x

Solution

ln (6) x + 4 (x ln (x) - x) + C

Solution steps

\int ln (6 x^{4}) d x

Simplify

ln (6 x^{4}) : ln (6) + 4 ln (x)

= \int ln (6) + 4 ln (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 ln (6) d x + \int 4 ln (x) d x

\int ln (6) d x = ln (6) x

\int 4 ln (x) d x = 4 (x ln (x) - x)

= ln (6) x + 4 (x ln (x) - x)

Add a constant to the solution

= ln (6) x + 4 (x ln (x) - x) + C

Popular Examples

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\int_{0}^{x} \frac{1}{x} d x

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\frac{d}{d x} (9 cos^{2} (x))

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\int 5 x^{2} d x

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x \to 0 lim (\frac{3 - 3}{x})

sum from k=1 to infinity of (2k+1)/k

k = 1 \sum \infty \frac{2 k + 1}{k}

Frequently Asked Questions (FAQ)

What is the integral of ln(6x^4) ?
The integral of ln(6x^4) is ln(6)x+4(xln(x)-x)+C