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).`
Find an anti derivative (or integral) of the following function by the method of inspection.
e2x
Find the following integrals:
`int(sqrtx - 1/sqrtx)^2 dx`
Find the following integrals:
`int(2x - 3cos x + e^x) dx`
Find the following integrals:
`int (2 - 3 sinx)/(cos^2 x) dx.`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
Integrate the function:
`1/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`
Integrate the function:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
`e^x/((1+e^x)(2+e^x))`
Integrate the function:
`1/((x^2 + 1)(x^2 + 4))`
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Integrate the function:
`tan^(-1) sqrt((1-x)/(1+x))`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
`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)` equals
`int (dx)/(x(x^2 + 1))` equals
`int sqrt(1 + x^2) dx` is equal to
If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.
In \[\int f(x)\,dx\], what is \(f(x)\) called?
In \[\int f(x)\,dx\], what is \(x\) called?
For \(n\ne -1\), which is the correct integral of \(x^n\)?
Evaluate \[\int \sin x\,dx\]
Evaluate \[\int e^x\,dx\]
