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  • <img alt="\text { If } \int x^{26} \cdot(x-1)^{17} \cdot(5 x-3) d x=\frac{x^{27} \cdot(x-1)^{18}}{k}+C" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Ctext%20%7B%20If%20%7D%20%5C

\text { If } \int x^{26} \cdot(x-1)^{17} \cdot(5 x-3) d x=\frac{x^{27} \cdot(x-1)^{18}}{k}+C where C is a constant of integration , then the value of k is equal to

Option: 1

3


Option: 2

6


Option: 3

9


Option: 4

12


Answers (1)

best_answer

Differentiating both sides gives 

\begin{aligned} x^{26} \cdot(x-1)^{17}(5 x-3) & =\frac{1}{k}\left[x^{27} \cdot 18(x-1)^{17}+(x-1)^{18} 27 x^{26}\right] \\ \\& =\frac{x^{26}(x-1)^{17}}{k}[18 x+27(x-1)] \end{aligned}

                                                 \begin{aligned} &=\frac{x^{26}(x-1)^{17}}{k}(45 x-27) \\ \\&=9 \frac{x^{26}(x-1)^{17}}{k}(5 x-3) \\ \\& \Rightarrow \quad k=9 \end{aligned}

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SANGALDEEP SINGH

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