Advertisements
Advertisements
Question
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.
Options
`sec^2 (π/4 - x) + c`
`-sec^2 (π/4 - x) + c`
`log |sec(π/4 - x)| + c`
`- log |sec(π/4 - x)| + c`
Advertisements
Solution
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is `underlinebb(- log |sec(π/4 - x)| + c)`.
Explanation:
Let I = `int (tanx - 1)/(tanx + 1) dx`
= `- int (1 - tanx)/(1 + tanx)dx`
= `-int (tan π/4 - tanx)/(1 + tan π/4 tanx)dx`
= `-int tan(π/4 - x)dx`
= `-log |sec(π/4 - x)| + c`
APPEARS IN
RELATED QUESTIONS
Find :`int(x^2+x+1)/((x^2+1)(x+2))dx`
If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).
Find an anti derivative (or integral) of the following function by the method of inspection.
sin 2x
Find an anti derivative (or integral) of the following function by the method of inspection.
Cos 3x
Find an anti derivative (or integral) of the following function by the method of inspection.
e2x
Find an antiderivative (or integral) of the following function by the method of inspection.
sin 2x – 4 e3x
Find the following integrals:
`int (x^3 + 3x + 4)/sqrtx dx`
Find the following integrals:
`int(1 - x) sqrtx dx`
Find the following integrals:
`intsqrtx( 3x^2 + 2x + 3) dx`
Find the following integrals:
`int(2x^2 - 3sinx + 5sqrtx) dx`
Find the following integrals:
`intsec x (sec x + tan x) dx`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is ______.
Integrate the function:
`1/(x - x^3)`
Integrate the function:
`1/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`
Integrate the function:
`1/(x^2(x^4 + 1)^(3/4))`
Integrate the function:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
f' (ax + b) [f (ax + b)]n
Evaluate `int tan^(-1) sqrtx dx`
`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (xdx)/((x - 1)(x - 2))` equals
`int sqrt(1 + x^2) dx` is equal to
In \[\int f(x)\,dx\], what is \(f(x)\) called?
Evaluate \[\int \cos x\,dx\]
Evaluate \[\int \text{cosec} x\cot x\,dx\]
Which expression is an antiderivative of \[\frac{1}{\sqrt{1-x^2}}\]?
Which expression is also an antiderivative of \[\frac{1}{\sqrt{1-x^2}}\]?
Evaluate \[\int \frac{1}{x}\,dx\]
