What is the integral of xe^{x^2}+1/(xln(x)) ?

The integral of xe^{x^2}+1/(xln(x)) is 1/2 e^{x^2}+ln|ln(x)|+C

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integral of xe^{x^2}+1/(xln(x))

\int x e^{x^{2}} + \frac{1}{x ln ( x )} d x

\frac{1}{2} e^{x^{2}} + ln ∣ ln (x) ∣ + C

Solution steps

\int x e^{x^{2}} + \frac{1}{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 x e^{x^{2}} d x + \int \frac{1}{x ln ( x )} d x

\int x e^{x^{2}} d x = \frac{1}{2} e^{x^{2}}

\int \frac{1}{x ln ( x )} d x = ln ∣ ln (x) ∣

= \frac{1}{2} e^{x^{2}} + ln ∣ ln (x) ∣

Add a constant to the solution

= \frac{1}{2} e^{x^{2}} + ln ∣ ln (x) ∣ + C

What is the integral of xe^{x^2}+1/(xln(x)) ?
The integral of xe^{x^2}+1/(xln(x)) is 1/2 e^{x^2}+ln|ln(x)|+C