Balbharati Maharashtra State Board Std 12 Commerce Statistics Part 1 Digest Pdf

Chapter 5 Integration Ex 5.5 Questions and Answers.

Evaluate the following.

Question 1.
∫x log x
Solution:


Question 2.
∫x² e^4x dx
Solution:




Question 3.
∫x² e^3x dx
Solution:


Question 4.
\(\int x^{3} e^{x^{2}} d x\)
Solution:


Question 5.
\(\int e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right) d x\)
Solution:


Question 6.
\(\int e^{x} \frac{x}{(x+1)^{2}} d x\)
Solution:




Question 7.
\(\int e^{x} \frac{x-1}{(x+1)^{3}} d x\)
Solution:


Question 8.
\(\int e^{x}\left[(\log x)^{2}+\frac{2 \log x}{x}\right] d x\)
Solution:


Question 9.
\(\int\left[\frac{1}{\log x}-\frac{1}{(\log x)^{2}}\right] d x\)
Solution:




Question 10.
\(\int \frac{\log x}{(1+\log x)^{2}} d x\)
Solution: