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Indefinite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsIndefinite Integration1 Mark
MCQ
$\int \frac{e^{2 x}+e^{-2 x}}{e^x} \cdot d x=$
  • ✓
    $e^x-\frac{1}{3 e^{3 x}}+c$
  • B
    $e^x+\frac{1}{3 e^{3 x}}+c$
  • C
    $e^{-x}+\frac{1}{3 e^{3 x}}+c$
  • D
    $e^{-x}-\frac{1}{3 e^{3 x}}+c$
✓

Answer

Correct option: A.
$e^x-\frac{1}{3 e^{3 x}}+c$
$e^x-\frac{1}{3 e^{3 x}}+c$
Hint.
$\int \frac{e^{2 x}+e^{-2 x}}{e^x} d x$
$=\int e^x d x+\int e^{-3 x} d x $
$ =e^x+\frac{e^{-3 x}}{(-3)}+c$
$=e^x-\frac{1}{3 e^{3 x}}+c$.

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