We can solve the integral $\int\sqrt{x}\ln\left(x\right)dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula
$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $\frac{1}{2}$
$\frac{1}{\frac{3}{2}}\sqrt{x^{3}}$
Intermediate steps
6
Now replace the values of $u$, $du$ and $v$ in the last formula
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more