Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.9

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Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.9

Integrate the following with respect to x
Question 1.
e^x (tan x + log sec x)
Solution:

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

Question 3.
e^x sec x (1 + tan x)
Solution:
Let I = \(\mathrm{I}=\int e^{x}(\sec x+\sec x \tan x) d x\)
Take f(x) = sec x
f ‘ (x) = sec x tan x
This is of the form of \(\int e^{x}\left[f(x)+f^{\prime}(x)\right] d x\) = e^x f(x) + c
= e^x sec x + c

Question 4.
e^x \(\left(\frac{2+\sin 2 x}{1+\cos 2 x}\right)\)
Solution:

Question 5.

Solution:

Question 6.

Solution: