Home
Class 12
MATHS
Choose the correct answerintx^2e^(x^3)dx...

Choose the correct answer`intx^2e^(x^3)dx`equals
(A) `1/3e^(x^3) +C` (B) `1/3e^(x^2)+C` (C) `1/2e^(x^3)+C` (D) `1/2e^(x^2)+C`

Text Solution

AI Generated Solution

To solve the integral \( \int x^2 e^{x^3} \, dx \), we can use the method of substitution. Here are the steps: ### Step-by-Step Solution: 1. **Substitution**: Let \( t = x^3 \). Then, we differentiate \( t \) with respect to \( x \): \[ dt = 3x^2 \, dx \quad \Rightarrow \quad dx = \frac{dt}{3x^2} \] ...
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.10|10 Videos

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.7|14 Videos

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.9|22 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT|Exercise EXERCISE 9.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise MISCELLANEOUS EXERCISE|17 Videos

Similar Questions

Explore conceptually related problems

int x^2 . e^(x^3) dx = (a) e^(x^3) + C (b) e^(x^2) + C (c) 1/3 e^(x^3) + C (d) 1/3 e^(x^2) + C

Choose the correct answers int(dx)/(e^x+e^(-x)) is equal to (A) tan^(-1)(e^x)+C (B) tan^(-1)(e^(-x))+C (C) log(e^x-e^(-x))+C (D) log(e^x+e^(-x))+C

If intx^(2).e^(x^(3))dx=u.e^(x^(3))+c, then u=

Choose the correct answer of the given question int (e^x+1)/(e^x-1) dx = ___ +c

(xe^x)/(1+x)^2dx= (A) e^x/(1+x) (B) e^x/(1+x)^2 (C) e^xlog(1+x) (D) none of these

The value of the integral int_-a^a (x e^(x^2))/(1+x^2)dx is (A) e^(a^2) (B) 0 (C) e^(-a^2) (D) a

The solution of y(2xy+e^x)dx-e^xdy=0 is (A) x^2+ye^(-x)=C (B) xy^2+e^(-x)=C (C) x/y+e^(-x)/x^2=C (D) x^2+e^x/y=C

The general solution of the differential equation (d^2y)/dx^2=e^(-3x) is (A) y=9e^(-3x)+C_1x+C_2 (B) y=-3e^(-3x)+C_1x+C_2 (C) y=3e^(-3x)+C_1x+C_2 (D) y=e^(-3x)/9+C_1x+C_2

int(2)/((e^(x)+e^(-x))^(2))dx(e^(-x))/(e^(x)+e^(-x))+C(b)-(1)/(e^(x)+e^(-x))+C(c)(-1)/((e^(x)+1)^(2))+C(d)(1)/(e^(x)-e^(-x))+C