Advertisements
Advertisements
Question
Integrate the function:
`cos^3 xe^(log sinx)`
Advertisements
Solution
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
RELATED QUESTIONS
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 the following integrals:
`int (4e^(3x) + 1)`
Find the following integrals:
`int(sqrtx - 1/sqrtx)^2 dx`
Find the following integrals:
`int(2x - 3cos x + e^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/(x^2(x^4 + 1)^(3/4))`
Integrate the function:
`1/(x^(1/2) + x^(1/3)) ["Hint:" 1/(x^(1/2) + x^(1/3)) = 1/(x^(1/3)(1+x^(1/6))), "put x" = t^6]`
Integrate the function:
`sinx/(sin (x - a))`
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the function:
`e^x/((1+e^x)(2+e^x))`
Integrate the function:
f' (ax + b) [f (ax + b)]n
Integrate the function:
`sqrt((1-sqrtx)/(1+sqrtx))`
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`
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 (dx)/(sin^2x cos^2x) dx` equals
`int (dx)/(x(x^2 + 1))` equals
`int e^x sec x(1 + tanx) dx` equals
`int sqrt(1 + x^2) dx` is equal to
`int sqrt(x^2 - 8x + 7) dx` is equal to:-
`d/(dx)x^(logx)` = ______.
If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.
Which statement about indefinite integrals is correct?
Evaluate \[\int \sin x\,dx\]
Evaluate \[\int \sec x\tan x\,dx\]
Evaluate \[\int \text{cosec} x\cot x\,dx\]
Which expression is also an antiderivative of \[\frac{1}{\sqrt{1-x^2}}\]?
Evaluate \[\int e^x\,dx\]
Evaluate \[\int \frac{1}{x}\,dx\]
Evaluate \[\int a^x\,dx\]
