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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Indefinite Integration

NDA 2012 · Mathematics · Indefinite Integration

What is ∫(x^2+1)^ (5)/(2) x d x equal to?

What is ∫(x2+1)52xdx\int\left(x^2+1\right)^{\frac{5}{2}} x d x equal to?

Options

  1. A(x2+1)72+c\left(x^2+1\right)^{\frac{7}{2}}+c
  2. B27(x2+1)72+c\frac{2}{7}\left(x^2+1\right)^{\frac{7}{2}}+c
  3. C17(x2+1)72+c\frac{1}{7}\left(x^2+1\right)^{\frac{7}{2}}+c
  4. DNone of the above

Correct answer

C. 17(x2+1)72+c\frac{1}{7}\left(x^2+1\right)^{\frac{7}{2}}+c

Step-by-step solution

Put x2+1=tx^2+1=t2x=dx=dtxdx=dt2∫(t)5/2dt2(C)12t7/27/2+c=17(x2+1)7/2+c\begin{aligned} & 2 x=d x=d t \\ & x d x=\frac{d t}{2} \quad \int(t)^{5 / 2} \frac{d t}{2}(C) \\ & \frac{1}{2} \frac{t^{7 / 2}}{7 / 2}+c=\frac{1}{7}\left(x^2+1\right)^{7 / 2}+c \end{aligned}$$
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