Advertisements
Advertisements
प्रश्न
Find the following integrals:
`int(2x^2 + e^x)dx`
Advertisements
उत्तर
Let I = `int (2x^2 + e^x) dx`
`= 2 int x^2 dx + int e^x dx`
`I =(2x^3)/3 + e^x + C`
APPEARS IN
संबंधित प्रश्न
If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).
Find an antiderivative (or integral) of the following function by the method of inspection.
sin 2x – 4 e3x
Find the following integrals:
`intx^2 (1 - 1/x^2)dx`
Find the following integrals:
`int (x^3 + 5x^2 -4)/x^2 dx`
Find the following integrals:
`int (x^3 - x^2 + x - 1)/(x - 1) dx`
Find the following integrals:
`int(2x - 3cos x + e^x) dx`
Find the following integrals:
`int(2x^2 - 3sinx + 5sqrtx) 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/(sqrt(x+a) + sqrt(x+b))`
Integrate the function:
`1/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`
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:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
`sinx/(sin (x - a))`
Integrate the function:
`x^3/(sqrt(1-x^8)`
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:
`sqrt((1-sqrtx)/(1+sqrtx))`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
Evaluate `int tan^(-1) sqrtx dx`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
Evaluate: `int (1 - cos x)/(cos x(1 + cos x)) dx`
The anti derivative of `(sqrt(x) + 1/sqrt(x))` is equals:
`sqrt((10x^9 + 10^x log e^10)/(x^10 + 10^x)) dx` equals
`int (dx)/(sin^2x cos^2x) dx` equals
`int (dx)/sqrt(9x - 4x^2)` equal
`int (xdx)/((x - 1)(x - 2))` equals
`int x^2 e^(x^3) dx` equals
`int e^x sec x(1 + tanx) dx` equals
`int sqrt(x^2 - 8x + 7) dx` is equal to:-
What is anti derivative of `e^(2x)`
`d/(dx)x^(logx)` = ______.
