IGNOU MTE 3 2018 - Evaluate the following integrals:i) ii) ∫ x ln | x + 1| dx

Question

Evaluate the following integrals:

i) Image ignouacademy-com--p-integrals-86255

ii) ∫ x ln | x + 1| dx

02 Feb 2018

Answer :

Word Count : 342

### Part i) The integral is: \[ \int \frac{1}{x^2 + 4} \, dx \] This is a standard integral. Recall that: \[ \int \frac{1}{x^2 + a^2} \, dx = \frac{1}{a} \arctan\left(\frac{x}{a}\right) + C \] Here, \( a = 2 \), so the integral becomes: \[ \int \frac{1}{x^2 + 4} \, dx = \frac{1}{2} \arctan\left(\frac{x}{2}\right) + C \] --- ### Part ii) The integral is: \[ \int x \ln|x + 1| \, dx \] This integral can be solved using

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