Advertisements
Advertisements
Question
`int x^2 e^(x^3) dx` equals
Options
`1/3 e^(x^3) + C`
`1/3 e^(x^4) + C`
`1/2 e^(x^3) + C`
`1/2 e^(x^2) + C`
Advertisements
Solution 1
`bb(1/3 e^(x^3) + C)`
Explanation:
`int x^2 e^(x^3) dx` put x3 = t
∴ 3x2 dx = dt
= `1/3 int (3x^2) e^(x^3) dx`
= `1/3 int e^t dt`
= `1/3 e^t + C`
= `1/3 e^(x^3) + C`
Solution 2
`bb(1/3 e^(x^3) + C)`
Explanation:
Given `int x^2 e^(x^3) dx`
Put x3 = y
⇒ 3x2dx = dy
Then `int x^2 e^(x^3) dx = 1/3 int e^y dy`
= `1/3 e^y + C`
= `1/3 e^(x^3) + C`
APPEARS IN
RELATED QUESTIONS
Write the antiderivative of `(3sqrtx+1/sqrtx).`
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.
sin 2x
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:
`intx^2 (1 - 1/x^2)dx`
Find the following integrals:
`intsqrtx( 3x^2 + 2x + 3) dx`
Find the following integrals:
`int(2x - 3cos x + e^x) dx`
If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is ______.
Integrate the function:
`1/(x^2(x^4 + 1)^(3/4))`
Integrate the function:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`(sin^8 x - cos^8 x)/(1-2sin^2 x cos^2 x)`
Integrate the function:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`
Integrate the function:
`(2+ sin 2x)/(1+ cos 2x) e^x`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Evaluate `int tan^(-1) sqrtx dx`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
`int (dx)/sqrt(9x - 4x^2)` equal
`int (xdx)/((x - 1)(x - 2))` equals
`int e^x sec x(1 + tanx) dx` equals
What is anti derivative of `e^(2x)`
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 ______.
`d/(dx)x^(logx)` = ______.
