Integrate the following with respect to x: eex(2+sin2x1+cos2x)

प्रश्न

Integrate the following with respect to x:

`"e"^x ((2 + sin 2x)/(1 + cos 2x))`

बेरीज

उत्तर

I = `int "e"^x ((2 + sin 2x)/(1 + cos 2x)) "d"x`

I = `int "e"^x ((2 + 2 sin x cos x)/(2 cos^2 x)) "d"x`

I = `int "e"^x ((2(1 + sin x cos x))/(2 cos^2x)) "d"x`

I = `int "e"^x ((1 + sin x cos x)/(cos^2x)) "d"x`

I = `int "e"^x [1/(cos^2x) + (sin x cos x)/(cos^2x)] "d"x`

I = `int "e"^x [sec^2x + sinx/cosx] "d"x`

I = `int "e"^x [sec^2x + tan x] "d"x`

I = `int "e"^x [tan x + sec^2x] "d"x`

Take f(x) = tan x

f'(x) = sec² x

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

I = e^x tan x + c

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Indefinite Integration with Standard Indefinite Integral Formulae - Methods of Integration

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Q 4 Q 3 Q 5

पाठ 11: Integral Calculus - Exercise 11.9 [पृष्ठ २१३]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board

पाठ 11 Integral Calculus
Exercise 11.9 | Q 4 | पृष्ठ २१३

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