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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Indefinite Integration

NDA 2021 · Mathematics · Indefinite Integration

What is ∫ e^ (2 x+ x^2) d x equal to?

What is ∫e(2ln⁡x+ln⁡x2)dx\int e^{\left(2 \ln x+\ln x^2\right)} d x equal to?

Options

  1. Ax44+c\frac{x^4}{4}+c
  2. Bx33+c\frac{x^3}{3}+c
  3. C2x55+c\frac{2 x^5}{5}+c
  4. Dx55+c\frac{x^5}{5}+c

Correct answer

D. x55+c\frac{x^5}{5}+c

Step-by-step solution

I=∫e(2ln⁡x+ln⁡x2)⋅dx=∫e(ln⁡x+ln⁡x2)⋅dx=∫e(2⋅ln⁡x2)⋅dx\begin{aligned} & \mathrm{I}=\int e^{\left(2 \ln x+\ln x^2\right)} \cdot d x \\ & =\int e^{\left(\ln x+\ln x^2\right)} \cdot d x=\int e^{\left(2 \cdot \ln x^2\right)} \cdot d x\end{aligned}=\int e^{\left(\ln x^4\right)} \cdot d x=\int x^4 \cdot d x=\frac{x^5}{5}+c$
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