AP EAMCET · Maths · Indefinite Integration
If \(\int x^3 e^{5 x} d x=\frac{e^{5 x}}{5^4}[f(x)]+C\), then \(f(x)\) is equal to
- A \(\frac{x^3}{5}-\frac{3 x^2}{5^2}+\frac{6 x}{5^3}-\frac{6}{5^4}\)
- B \(5 x^3-5^2 x^2+5^3 x-6\)
- C \(5^2 x^3-15 x^2+30 x-6\)
- D \(5^3 x^3-75 x^2+30 x-6\)
Answer & Solution
Correct Answer
(D) \(5^3 x^3-75 x^2+30 x-6\)
Step-by-step Solution
Detailed explanation
We have given that, \(\int x^3 e^{5 x} d x=\frac{e^{5 x}}{5^4}\left[\int(x)\right]+c\) By using the method of intergration by parts, we get…
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