Advertisements
Advertisements
प्रश्न
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.
विकल्प
`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
उत्तर
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
संबंधित प्रश्न
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 anti derivative (or integral) of the following function by the method of inspection.
(axe + b)2
Find an antiderivative (or integral) of the following function by the method of inspection.
sin 2x – 4 e3x
Find the following integrals:
`int (ax^2 + bx + c) dx`
Find the following integrals:
`int(2x^2 + e^x)dx`
Find the following integrals:
`int(sqrtx - 1/sqrtx)^2 dx`
Find the following integrals:
`int (x^3 + 3x + 4)/sqrtx dx`
Find the following integrals:
`int(1 - x) sqrtx dx`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
Integrate the function:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`1/((x^2 + 1)(x^2 + 4))`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Integrate the function:
`(sqrt(x^2 +1) [log(x^2 + 1) - 2log x])/x^4`
`int (dx)/sqrt(9x - 4x^2)` equal
`int sqrt(1 + x^2) dx` is equal to
What is anti derivative of `e^(2x)`
If the normal to the curve y(x) = `int_0^x(2t^2 - 15t + 10)dt` at a point (a, b) is parallel to the line x + 3y = –5, a > 1, then the value of |a + 6b| is equal to ______.
`d/(dx)x^(logx)` = ______.
What is integration?
What is \(C\) called in \[\int f(x)\,dx=F(x)+C\]?
Which antiderivative has derivative \(1\)?
Evaluate \[\int \text{cosec} x\cot x\,dx\]
Which expression is an antiderivative of \[\frac{1}{\sqrt{1-x^2}}\]?
Evaluate \[\int \frac{dx}{1+x^2}\]
