If ∫(ax+x+sec2x)dx=axlogk+p⋅x1p+tanx+c, then p+k=

∫axdx+∫x⋅dx+∫sec2x⋅dx=axloga+23⋅x3/2+tanx+c∴k=a, p=23

∫axdx+∫x⋅dx+∫sec2x⋅dx=axloga+23⋅x3/2+tanx+c∴k=a, p=23

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If $\int (a^{x} + \sqrt{x} + \sec^{2} x) d x = \frac{a^{x}}{\log k} + p \cdot x^{\frac{1}{p}} + \tan x + c$ , then $p + k =$

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$\frac{2 a - 3}{2}$

$\frac{2 a + 3}{2}$

$\frac{3 a - 2}{3}$

$\frac{3 a + 2}{3}$

answer is A.

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$\int a^{x} d x + \int \sqrt{x} \cdot d x + \int \sec^{2} x \cdot d x$

$= \frac{a^{x}}{\log a} + \frac{2}{3} \cdot x^{3 / 2} + \tan x + c$

$∴ k = a, p = \frac{2}{3}$

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