COMEDK · Maths · 28. Indefinite Integration
\(\int e^{x} \cdot x^{5} d x\) is
- A \(e^{x}\left[x^{5}+5 x^{4}+20 x^{3}+60 x^{2}+120 x+120\right]+C\)
- B \(e^{x}\left[x^{5}-5 x^{4}-20 x^{3}-60 x^{2}-120 x-120\right]+C\)
- C \(e^{x}\left[x^{5}-5 x^{4}+20 x^{3}-60 x^{2}+120 x-120\right]+C\)
- D \(e^{x}\left[x^{5}+5 x^{4}+20 x^{3}-60 x^{2}-120 x+120\right]+C\)
Answer & Solution
Correct Answer
(C) \(e^{x}\left[x^{5}-5 x^{4}+20 x^{3}-60 x^{2}+120 x-120\right]+C\)
Step-by-step Solution
Detailed explanation
Let \(I=\int e_{\text {II II }}^{x} \cdot x^{5} d x\) \(=x^{5} \cdot e^{x}-\int e^{x} \cdot\left(5 x^{4}\right) d x\) \(=x^{5} e^{x}-5 \int e^{x} \cdot x^{4} d x\) \(=x^{5} e^{x}-5\left[x^{4} \cdot e^{x}-\int e^{x} \cdot 4 x^{3} d x\right]\)…
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