Advertisements
Advertisements
प्रश्न
Integrate the function:
`(sin^8 x - cos^8 x)/(1-2sin^2 x cos^2 x)`
Advertisements
उत्तर
Let `I = int (sin^8 x - cos^8 x)/ (1 - 2 sin^2x cos^2 x) dx`
We have, (sin8x - cos8x)
= (sin4x + cos4x) (sin4x - cos4x)
= [(sin2x + cos2x)2 - 2 sin2x cos2 x] (sin2 x + cos2 x) (sin2 x - cos2 x)
= (1 - 2 sin2x cos2x) (1) (-cos2x)
∴ `I = int ((1 - 2 sin^2 x cos^2 x) (- cos 2x))/(1 - 2 sin^2 x cos x) dx`
`= - int cos 2x dx`
`= -1/2 sin2x + C`
APPEARS IN
संबंधित प्रश्न
Write the antiderivative of `(3sqrtx+1/sqrtx).`
If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).
Find the following integrals:
`int (ax^2 + bx + c) dx`
Find the following integrals:
`int (x^3 + 5x^2 -4)/x^2 dx`
Find the following integrals:
`int (x^3 + 3x + 4)/sqrtx dx`
Find the following integrals:
`int (x^3 - x^2 + x - 1)/(x - 1) dx`
Find the following integrals:
`int(2x^2 - 3sinx + 5sqrtx) dx`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
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:
`(e^(5log x) - e^(4log x))/(e^(3log x) - e^(2log x))`
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`cos^3 xe^(log sinx)`
Integrate the function:
`1/sqrt(sin^3 x sin(x + alpha))`
Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`
Integrate the function:
`sqrt((1-sqrtx)/(1+sqrtx))`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Evaluate `int tan^(-1) sqrtx dx`
Evaluate: `int (1 - cos x)/(cos x(1 + cos x)) dx`
If `d/(dx) f(x) = 4x^3 - 3/x^4`, such that `f(2) = 0`, then `f(x)` is
`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (e^x (1 + x))/(cos^2 (xe^x)) dx` equal
`int x^2 e^(x^3) dx` equals
What is anti derivative of `e^(2x)`
In \[\int f(x)\,dx\], what is \(f(x)\) called?
What is \(C\) called in \[\int f(x)\,dx=F(x)+C\]?
Which statement about indefinite integrals is correct?
Which antiderivative has derivative \(1\)?
Evaluate \[\int \sec^2 x\,dx\]
Evaluate \[\int \text{cosec}^2 x\,dx\]
Evaluate \[\int \sec x\tan x\,dx\]
Evaluate \[\int \frac{1}{x}\,dx\]
Evaluate \[\int a^x\,dx\]
