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Question
`int ("e"^x(1 + x))/(cos^2 ("e"^x x))"d"x` is equals to ______.
Options
– cot (exx) + C
tan (xex) + C
tan (ex) + C
cot (ex) + C
MCQ
Fill in the Blanks
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Solution
`int ("e"^x(1 + x))/(cos^2 ("e"^x x))"d"x` is equals to tan (xex) + C.
Explanation:
`int ("e"^x(1 + x))/(cos^2 ("e"^x x))"d"x`
Let xex = t
`\implies` (xex + ex) = `("dt")/("d"x)`
`\implies` dx = `("dt")/("e"^x(x + 1))`
∴ `int ("e"^x(1 + x))/(cos^2("e"^x x))"d"x = int ("e"^x(1 + x))/(cos^2"t") xx ("dt")/("e"^x(1 + x))`
= `int 1/(cos^2"t")"dt"`
= `int sec^2"t" "dt"`
= tan t + C
= tan (xex) + C
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Integrals of Trignometric Functions
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