Advertisements
Advertisements
Question
Find an anti derivative (or integral) of the following function by the method of inspection.
Cos 3x
Solution
We know that,
`d/dx` sin 3x = 3 cos 3x
or cos 3x = `d/dx(1/3 sin 3x)`
Hence, the antiderivative of cos 3x is `1/3` sin 3x.
APPEARS IN
RELATED QUESTIONS
Write the antiderivative of `(3sqrtx+1/sqrtx).`
Find an anti derivative (or integral) of the following function by the method of inspection.
(axe + b)2
Find the following integrals:
`int (ax^2 + bx + c) dx`
Find the following integrals:
`intsqrtx( 3x^2 + 2x + 3) dx`
Find the following integrals:
`int(2x - 3cos x + e^x) 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/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`
Integrate the function:
`sinx/(sin (x - a))`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the function:
`e^x/((1+e^x)(2+e^x))`
Integrate the function:
`1/((x^2 + 1)(x^2 + 4))`
Integrate the function:
`cos^3 xe^(log sinx)`
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
Integrate the function:
f' (ax + b) [f (ax + b)]n
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))`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
Evaluate: `int (1 - cos x)/(cos x(1 + cos x)) dx`
The anti derivative of `(sqrt(x) + 1/sqrt(x))` is equals:
If `d/(dx) f(x) = 4x^3 - 3/x^4`, such that `f(2) = 0`, then `f(x)` is
`int (dx)/(sin^2x cos^2x) dx` 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
`int (dx)/sqrt(9x - 4x^2)` equal
`int (xdx)/((x - 1)(x - 2))` equals
`f x^2 e^(x^3) dx` equals
`int sqrt(1 + x^2) dx` is equal to
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 ______.
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 ______.
