In this page integration worksheet1 solution1 we are going to see solution of some practice question from the worksheet of integration.

**Question 1**

Integrate the following with respect to x , x¹⁶

**Solution:**

The given question exactly matches the formula

**∫ xⁿ dx = x⁽ⁿ ⁺ ¹⁾/(n + 1) + c**

now we are going to integrate the given question bu using this formula in the question instead of n we have 16

So we get,

∫ x¹⁶ dx = x^(16+1)/(16+1)

= (x^17/17) + C

**Question 2**

Integrate the following with respect to x , x^(5/2)

**Solution:**

The given question exactly matches the formula

**∫ xⁿ dx = x⁽ⁿ ⁺ ¹⁾/(n + 1) + c**

So now we are going to integrate the given question bu using this formula in the question instead of n we have 5/2

So we get,

∫ x^(5/2) dx = x^[(5/2)+1]/[(5/2) + 1]

= x^[(5 + 2)/2]/[(5+2)/2]

= x^[7/2]/[7/2]

= (2/7)x^(7/2) + C

**Question 3**

Integrate the following with respect to x , √x⁷

**Solution:**

√x⁷ = x^7^(1/2)

= x^(7/2)

The given question exactly matches the formula

**∫ xⁿ dx = x⁽ⁿ ⁺ ¹⁾/(n + 1) + c**

So now we are going to integrate the given question bu using this formula in the question instead of n we have 7/2

So we get,

∫ x^(7/2) dx = x^[(7/2)+1]/[(7/2) + 1]

= x^[(7 + 2)/2]/[(7+2)/2]

= x^[9/2]/[9/2]

= (2/9)x^(9/2) + C

**Question 4:**

Integrate the following with respect to x , ∛x⁴

**Solution:**

∛x⁴ = x^4^(1/3)

= x^(4/3)

The given question exactly matches the formula

**∫ xⁿ dx = x⁽ⁿ ⁺ ¹⁾/(n + 1) + c**

So now we are going to integrate the given question bu using this formula in the question instead of n we have 4/3

So we get,

∫ x^(4/3) dx = x^[(4/3)+1]/[(4/3) + 1]

= x^[(4 + 3)/3]/[(4+3)/3]

= x^[7/3]/[7/3]

= (3/7)x^(7/3) + C

**Question 5:**

Integrate the following with respect to x , (x^10)^(1/7)

**Solution:**

(x^10)^(1/7) = x^(10/7)

The given question exactly matches the formula

**∫ xⁿ dx = x⁽ⁿ ⁺ ¹⁾/(n + 1) + c**

So now we are going to integrate the given question bu using this formula in the question instead of n we have 10/7

So we get,

∫ x^(10/7) dx = x^[(10/7)+1]/[(10/7) + 1]

= x^[(10 + 7)/7]/[(10+7)/7]

= x^[17/7]/[17/7]

= (7/17)x^(17/7) + C

integration worksheet1 solution1 integration worksheet1 solution1

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- Integration
- Substitution method
- Decomposition method
- Properties of integrals
- Integration-by parts
- Integration-of Sec³ x
- Standard integrals
- Integrating quadratic denominator
- Integration-using partial fractions
- Definite integrals