What is the integral of x^{2x}(1+ln(x)) ?

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

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integral of x^{2x}(1+ln(x))

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

\frac{1}{2} x^{2 x} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{2} d u

= \int \frac{1}{2} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{2} u

Substitute back

u = x^{2 x}

= \frac{1}{2} x^{2 x}

Add a constant to the solution

= \frac{1}{2} x^{2 x} + C

\int (1 + 7 x)^{\frac{1}{3}} d x

\int 6 x + 6 d x

\int x \cdot 2 e^{- 2 x} d x

\int - 6 x d x

\int \frac{2}{x ^{\frac{1}{3}}} d x

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