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## Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6

Integrate the following with respect to x.

Question 1.

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

Solution:

Question 2.

\(\frac{x^{2}}{1+x^{6}}\)

Solution:

Question 3.

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

Solution:

Question 4.

Solution:

Question 5.

\(\frac{\sin \sqrt{x}}{\sqrt{x}}\)

Solution:

Question 6.

\(\frac{\cot x}{\log (\sin x)}\)

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

\(\frac{\sqrt{x}}{1+\sqrt{x}}\)

Solution:

Question 11.

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

Solution:

Question 12.

αβx^{α-1}e^{-βxα}

Solution:

Question 13.

\(\tan x \sqrt{\sec x}\)

Solution:

Question 14.

x(1 – x)^{17}

Solution:

Question 15.

sin^{5} x cos^{3} x

Solution:

Question 16.

\(\frac{\cos x}{\cos (x-a)}\)

Solution:

### Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 Additional Problems

Question 1.

(2x + 3)\(\sqrt{x^{2}+3 x-5}\)

Solution:

Question 2.

\(\frac{x \sin ^{-1}\left(x^{2}\right)}{\sqrt{1-x^{4}}}\)

Solution:

Question 3.

sec4 x tan x

Solution:

Question 4.

\(\frac{\sin x}{\sin (x+a)}\)

Solution:

Question 5.

\(\frac{\sqrt{\tan x}}{\sin x \cos x}\)

Solution:

Question 6.

x(l – x)^{16}

Solution:

Question 7.

x^{2}(2 – x)^{15}

Solution:

Question 8.

(x + 1)\(\sqrt{2 x+3}\)

Solution:

Question 9.

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

Solution: