Step-by-step Solution

Calculate the integral $\int\sqrt{x}\ln\left(x\right)dx$

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Step-by-step explanation

Problem to solve:

$\int\sqrt{x}\ln\left(x\right)dx$

Learn how to solve integrals with radicals problems step by step online.

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

Unlock this full step-by-step solution!

Learn how to solve integrals with radicals problems step by step online. Calculate the integral int(x^0.5*ln(x))dx. 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. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

Final Answer

$\frac{2}{3}\sqrt{x^{3}}\ln\left(x\right)-\frac{4}{9}\sqrt{x^{3}}+C_0$