COMEDK · Maths · 28. Indefinite Integration
The value of \(\int e^{x^5} \cdot x^4 d x\) is
- A \(e^{x^5}+C\)
- B \(5 e^{x^5}+C\)
- C \(\frac{e^{x^5}}{5}+C\)
- D None of these
Answer & Solution
Correct Answer
(C) \(\frac{e^{x^5}}{5}+C\)
Step-by-step Solution
Detailed explanation
Let \(x^5=t\) Differentiate both sides w.r.t. \(x\), \(5 x^4 d x =d t\) \(x^4 d x =\frac{d t}{5}\) \(\int e^{x^5} x^4 d x =\int e^t \frac{d t}{5}\) \(=\frac{1}{5} \int e^t d t \left[\because \int e^t d t=e^t+C\right]\) \(=\frac{1}{5} e^t+C=\frac{1}{5} e^{x^5}+C\)
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