Advertisements
Advertisements
प्रश्न
Integrate the function:
`cos^3 xe^(log sinx)`
Advertisements
उत्तर
Let `I = cos^3 x e^(log sinx) dx`
`= int cos^3 x sin x` dx
Substituting cos x = t,
⇒ - sin x dx = dt
⇒ sin x dx = - dt
Hence, `I = - int t^3 dt`
`= - t^4/4 + C`
`= - 1/4 cos^4 x + C`
APPEARS IN
संबंधित प्रश्न
Write the antiderivative of `(3sqrtx+1/sqrtx).`
Evaluate : `∫(sin^6x+cos^6x)/(sin^2x.cos^2x)dx`
Find :`int(x^2+x+1)/((x^2+1)(x+2))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 (ax^2 + bx + c) dx`
Find the following integrals:
`int(2x^2 + e^x)dx`
Find the following integrals:
`int (x^3 + 5x^2 -4)/x^2 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:
`int (2 - 3 sinx)/(cos^2 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:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`1/sqrt(sin^3 x sin(x + alpha))`
Integrate the function:
`(2+ sin 2x)/(1+ cos 2x) e^x`
Integrate the function:
`tan^(-1) sqrt((1-x)/(1+x))`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
Evaluate: `int (1 - cos x)/(cos x(1 + cos x)) dx`
`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (dx)/sqrt(9x - 4x^2)` equal
`int sqrt(1 + x^2) dx` is equal to
`int sqrt(x^2 - 8x + 7) dx` is equal to:-
What is anti derivative of `e^(2x)`
`int (dx)/sqrt(5x - 6 - x^2)` equals ______.
In \[\int f(x)\,dx\], what is \(f(x)\) called?
What is “an integral of \(f\)” ?
What is \(C\) called in \[\int f(x)\,dx=F(x)+C\]?
For \(n\ne -1\), which is the correct integral of \(x^n\)?
Evaluate \[\int \sec x\tan x\,dx\]
Which expression is an antiderivative of \[\frac{1}{\sqrt{1-x^2}}\]?
Evaluate \[\int \frac{dx}{1+x^2}\]
