What is the integral of (100x^4+1)ln(x) ?

The integral of (100x^4+1)ln(x) is 100(1/5 x^5ln(x)-(x^5)/(25))+xln(x)-x+C

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integral of (100x^4+1)ln(x)

\int (100 x^{4} + 1) ln (x) d x

100 (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}) + x ln (x) - x + C

Solution steps

\int (100 x^{4} + 1) ln (x) d x

Expand

(100 x^{4} + 1) ln (x) : 100 x^{4} ln (x) + ln (x)

= \int 100 x^{4} ln (x) + 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 100 x^{4} ln (x) d x + \int ln (x) d x

\int 100 x^{4} ln (x) d x = 100 (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25})

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

= 100 (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}) + x ln (x) - x

Add a constant to the solution

= 100 (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}) + x ln (x) - x + C

What is the integral of (100x^4+1)ln(x) ?
The integral of (100x^4+1)ln(x) is 100(1/5 x^5ln(x)-(x^5)/(25))+xln(x)-x+C