Advertisements
Advertisements
Question
Integrate the function:
`(sin^8 x - cos^8 x)/(1-2sin^2 x cos^2 x)`
Advertisements
Solution
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
RELATED QUESTIONS
Evaluate : `∫(sin^6x+cos^6x)/(sin^2x.cos^2x)dx`
Find an anti derivative (or integral) of the following function by the method of inspection.
Cos 3x
Find an antiderivative (or integral) of the following function by the method of inspection.
sin 2x – 4 e3x
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`
Find the following integrals:
`int(sec^2x)/(cosec^2x) dx`
Find the following integrals:
`int (2 - 3 sinx)/(cos^2 x) dx.`
Integrate the function:
`1/(x - x^3)`
Integrate the function:
`1/(sqrt(x+a) + sqrt(x+b))`
Integrate the function:
`1/(x^2(x^4 + 1)^(3/4))`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
Integrate the function:
`(2+ sin 2x)/(1+ cos 2x) e^x`
Integrate the function:
`tan^(-1) sqrt((1-x)/(1+x))`
Evaluate `int tan^(-1) sqrtx dx`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
The anti derivative of `(sqrt(x) + 1/sqrt(x))` is equals:
`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (e^x (1 + x))/(cos^2 (xe^x)) dx` equal
What is anti derivative of `e^(2x)`
If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.
`int (dx)/sqrt(5x - 6 - x^2)` equals ______.
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.
In \[\int f(x)\,dx\], what is \(x\) called?
What is integration?
Which statement about indefinite integrals is correct?
Which antiderivative has derivative \(1\)?
Evaluate \[\int \cos x\,dx\]
Evaluate \[\int \text{cosec}^2 x\,dx\]
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 \[\int a^x\,dx\]
