Indefinite Integration questions
503 published questions with worked solutions.
- The integral _ 4 ^ 3 4 dx 1 + x is equal to :
- The integral ^2 x ^2 x ( ^5 x + ^3 x ^2 x + ^3 x ^2 x + ^5 x)^2 ,dx is equal to (where C is a constant of integration)
- If x 1 + x + ^2 x ,dx = x - K A ^ -1 ( K x + 1 A ) + C, (C is a constant of integration), then the ordered pair (K, A) is equal...
- 5x 2 x 2 ,dx is equal to (where c is a constant of integration)
- The integral ^ 2/3 x , cosec ^ 4/3 x ,dx is equal to: (Here C is a constant of integration)
- The integral _ /6 ^ /3 ^ 2/3 x , cosec ^ 4/3 x ,dx is equal to:
- If x^5e^ -x^2 dx = g(x)e^ -x^2 + c, where c is a constant of integration, then g(−1) is equal to:
- If f ( x - 4 x + 2 ) = 2x + 1, (x R - 1, -2 ), then f(x) ,dx is equal to (where C is a constant of integration)
- 2x + 5 7 - 6x - x^2 ,dx = A 7 - 6x - x^2 + B ^ -1 ( x + 3 4 ) + C (where C is a constant of integration), then the ordered pair...
- If e^ x ( x x ,f(x) + ( x x + ^2x) )dx = e^ x f(x) + C, then a possible choice of f(x) is:
- If dx (x^2 - 2x + 10)^2 = A ( ^ -1 ( x-1 3 ) + f(x) x^2 - 2x + 10 ) + C where C is a constant of integration then:
- If f(x) = 5x^8 + 7x^6 (x^2 + 1 + 2x^7)^2 dx, (x ≥ 0), and f(0) = 0, then the value of f(1) is:
- If _0^ /3 2k d = 1 - 1 2 , (k > 0), then the value of k is:
- For x^2 n + 1, n ∈ N (the set of natural numbers), the integral x 2 (x^2-1) - 2(x^2-1) 2 (x^2-1) + 2(x^2-1) ,dx is equal to:...
- The integral 2x^3 - 1 x^4 + x dx is equal to: (Here C is a constant of integration)
- The integral _1^e ( xe )^ 2x - ( ex )^x _ex ,dx is equal to:
- The integral 3x^ 13 + 2x^ 11 (2x^4 + 3x^2 + 1)^4 dx is equal to: (where C is a constant of integration)
- The integral ( _ex) ,dx is equal to: (where C is a constant of integration)
- If x + 1 2x - 1 dx = f(x) 2x - 1 + C, where C is a constant of integration, then f(x) is equal to:
- If x^5e^ -4x^3 dx = 1 48 e^ -4x^3 f(x) + C, where C is a constant of integration, then f(x) is equal to:
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