Integrate the following with respect to x: eex(tanx+logsecx)

Integrate the following with respect to x:

`"e"^x (tan x + log sec x)`

Sum

Let I = `int "e"^x (tan x + log sec x) "d"x`

Take f(x) = log sec x

f'(x) = `1/sec x sec x tan x`

f'(x) = tan x

`[int"e"^x ["f"(x) + "f"(x)] "d"x = "e"^x"f"(x) + "c"]`

∴ I = e^x log |sec x| + c

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Chapter 11: Integral Calculus - Exercise 11.9 [Page 213]

Chapter 11 Integral Calculus
Exercise 11.9 | Q 1 | Page 213

Evaluate : `int1/(x(3+logx))dx`

Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`

Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx

Integrate the following functions with respect to x :

`(sin^2x)/(1 + cosx)`

Integrate the following functions with respect to x :

cos 3x cos 2x

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`1/((x - 1)(x + 2)^2`

Integrate the following with respect to x :

`(10x^9 + 10^x log_"e" 10)/(10^x + x^10)`

Integrate the following with respect to x :

`tan x sqrt(sec x)`

Integrate the following with respect to x :

x(1 – x)¹⁷

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9xe^3x

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`(x sin^-1 x)/sqrt(1 - x^2)`

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`tan^-1 ((8x)/(1 - 16x^2))`

Find the integrals of the following:

`1/(4 - x^2)`

Integrate the following functions with respect to x:

`sqrt(x^2 + 2x + 10)`

Integrate the following functions with respect to x:

`sqrt((6 - x)(x - 4))`