Question

`int(1 + logx)^3/xdx` = ______

पर्याय

• 4(1 + log x)⁴ + c 

• 3(1 +log x)³ + c

• `1/3(1 + logx)^3 + c`

• `1/4(1 + logx)^4 + c`

Answer 1

`int(1 + logx)^3/xdx` = `underline(1/4(1 + logx)^4 + c)`

Explanation:

Put (1 + logx) = t ⇒ `1/x`dx = dt

∴ `int(1 + logx)^3/xdx = intt^3 dt`

= `t^4/4 + c = 1/4(1 + logx)^4 + c`