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:

Question 2.

\(\frac{e^{3 \log x}}{x^{4}+1}\)

Solution:

Question 3.

\(\frac{e^{2 x}}{e^{2 x}-2}\)

Solution:

Question 4.

\(\frac{(\log x)^{3}}{x}\)

Solution:

Question 5.

\(\frac{6 x+7}{\sqrt{3 x^{2}+7 x-1}}\)

Solution:

Question 6.

\((4 x+2) \sqrt{x^{2}+x+1}\)

Solution:

\((4 x+2) \sqrt{x^{2}+x+1}\)

Let f(x) = x^{2} + x + 1

then f'(x) = 2x + 1

Question 7.

x^{8} (1 + x^{9})^{5}

Solution:

Question 8.

\(\frac{x^{e-1}+e^{x-1}}{x^{e}+e^{x}}\)

Solution:

Question 9.

\(\frac{1}{x \log x}\)

Solution:

Question 10.

\(\frac{x}{2 x^{4}-3 x^{2}-2}\)

Solution:

Question 11.

e^{x} (1 + x) log(x e^{x})

Solution:

∫e^{x}(1 + x) log (xe^{x}) dx

= ∫z (e^{z}) dz

= ∫udv = uv – u’v’

= (z) (e^{z}) – (1) (e^{z})

= e^{z} (z – 1) + c

= ei^{log(xex)} (log (xe^{x}) – 1) + c

= xe^{x} (log (xe^{x}) – 1) + c

Take z = log (xe^{x})

\(\frac { dz }{dx}\) = \(\frac { 1 }{xe^x}\) = (xe^{x} + e^{x})

xe^{x}dz = (xe^{x} + e^{x}) dx

xe^{x}dz = e^{x} (1 + x) dx

e^{z}dz = e^{x}(1 + x) dx

Question 12.

\(\frac{1}{x^{2}\left(x^{2}+1\right)}\)

Solution:

Question 13.

\(e^{x}\left[\frac{1}{x^{2}}-\frac{2}{x^{3}}\right]\)

Solution:

Question 14.

\(e^{x}\left[\frac{x-1}{(x+1)^{3}}\right]\)

Solution:

Question 15.

\(e^{3 x}\left[\frac{3 x-1}{9 x^{2}}\right]\)

Solution: