Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6

Students can download 12th Business Maths Chapter 2 Integral Calculus I Ex 2.6 Questions and Answers, Samacheer Kalvi 12th Business Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6

Integrate the following with respect to x.

Question 1.
\(\frac{2 x+5}{x^{2}+5 x-7}\)
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q1

Question 2.
\(\frac{e^{3 \log x}}{x^{4}+1}\)
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q2

Question 3.
\(\frac{e^{2 x}}{e^{2 x}-2}\)
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q3

Question 4.
\(\frac{(\log x)^{3}}{x}\)
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q4

Question 5.
\(\frac{6 x+7}{\sqrt{3 x^{2}+7 x-1}}\)
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q5

Question 6.
\((4 x+2) \sqrt{x^{2}+x+1}\)
Solution:
\((4 x+2) \sqrt{x^{2}+x+1}\)
Let f(x) = x2 + x + 1
then f'(x) = 2x + 1
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q6

Question 7.
x8 (1 + x9)5
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q7

Question 8.
\(\frac{x^{e-1}+e^{x-1}}{x^{e}+e^{x}}\)
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q8

Question 9.
\(\frac{1}{x \log x}\)
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q9

Question 10.
\(\frac{x}{2 x^{4}-3 x^{2}-2}\)
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q10
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q10.1

Question 11.
ex (1 + x) log(x ex)
Solution:
ex (1 + x) log(x ex) = (ex + x ex) log (x ex)
Let z = x ex, Then dz = d(x ex)
dz = (x ex + ex) dx (Using product rule)
So ∫ ex (1 + x) log (x ex) dx
= ∫ log (x ex) (ex + x ex) dx
= ∫ log z dz
= z (log z – 1) + c
= x ex [log (x ex) – 1] + c

Question 12.
\(\frac{1}{x^{2}\left(x^{2}+1\right)}\)
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q12

Question 13.
\(e^{x}\left[\frac{1}{x^{2}}-\frac{2}{x^{3}}\right]\)
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q13

Question 14.
\(e^{x}\left[\frac{x-1}{(x+1)^{3}}\right]\)
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q14

Question 15.
\(e^{3 x}\left[\frac{3 x-1}{9 x^{2}}\right]\)
Solution:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.6 Q15