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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: