Step-by-step Solution

Solve the integral of logarithmic functions $\int\ln\left(x+1\right)dx$

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Step-by-step Solution

Problem to solve:

$\int In\left(x+1\right)dx$

Solving method

Learn how to solve integrals involving logarithmic functions problems step by step online.

$u=x+1$

Unlock this full step-by-step solution!

Learn how to solve integrals involving logarithmic functions problems step by step online. Solve the integral of logarithmic functions int(ln(x+1))dx. We can solve the integral \int\ln\left(x+1\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x+1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Substituting u and dx in the integral and simplify. We can solve the integral \int\ln\left(u\right)du by applying integration by parts method to calculate the integral of the product of two functions, using the following formula.

Final Answer

$\left(x+1\right)\ln\left(x+1\right)-1-x+C_0$