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GUJCET · Maths · Integrals
\(\int(x+1)(x+3)(x+2)^7 d x=\) __________ \(+C\).
- A \(\frac{(x+2)^{10}}{10}-\frac{(x+2)^8}{8}\)
- B \(\frac{(x+2)^{10}}{10}+\frac{(x+2)^8}{8}\)
- C \(\frac{(x+3)^{10}}{10}-\frac{(x+3)^8}{8}\)
- D \(\frac{(x+3)^{10}}{10}+\frac{(x+3)^8}{8}\)
Answer & Solution
Correct Answer
(A) \(\frac{(x+2)^{10}}{10}-\frac{(x+2)^8}{8}\)
Step-by-step Solution
Detailed explanation
Let \(u=x+2\). \(\int (u-1)(u+1)u^7 du = \int (u^2-1)u^7 du = \int (u^9-u^7) du\).
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