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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $\int \large\frac{ax^3+bx+c}{\sqrt x}$$dx$

\[\begin {array} {1 1} (a)\;\frac{2}{7} ax^{7/2}+\frac{2}{3} x^{3/2}.b+ 2cx^{3/2} \\ (b)\;\frac{2}{7} ax^{-7/2}+\frac{2}{3}bx^{3/2}+ 2c \sqrt x+c+d \\ (c)\;\frac{2}{5} ax^{5/2}+2b x^{1/2}+ 2c+d \\ (d)\;None \end {array}\]

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A)
ax5/2+bx+c(x)1/2dx\int ax^{5/2} + b \sqrt {x} +c(x) ^{-1/2}dx
=> 27ax7/2+23 \large\frac{2}{7} \normalsize a x^{7/2}+\frac{2}{3}bx3/2bx^{3/2} +2cx+d+ 2 c \sqrt {x} +d
Hence b is the correct answer.
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