In this page integration worksheet1 solution2 we are going to see
solution of some practice question from the worksheet of integration.

**Question 6**

Integrate the following with respect to x , 1/x⁵

**Solution:**

1/x⁵ = x^(-5)

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

So we get,

∫ x^(-5) dx = x^(-5+1)/(-5+1)

= x^(-4)/(-4) + C

= -1/4x^4 + C

**Question 7**

Integrate the following with respect to x , x⁻¹

**Solution:**

x⁻¹ = 1/x

The given question exactly matches the formula

**∫ 1/x dx = log x + c**

So 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,

∫ 1/x dx = log x

= log x + C

**Question 8**

Integrate the following with respect to x , 1/x^(5/2)

**Solution:**

1/x^(5/2)
= x^(-5/2)

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 -5/2

So we get,

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

= x^(-3/2)/(-3/2) + C

= (-2/3)x^(-3/2) + C

= -2/3x^(3/2) + C

= -2/3x√x + C

**Question 9**

Integrate the following with respect to x , 1/∛x⁵

**Solution:**

1/∛x⁵ = 1/x^5^(1/3)

= x^(-5/3)

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 -5/3

So we get,

∫ x^(-5/3) dx = x^[(-5/3)+1)]/[(-5/3) + 1]

= x^[(-5 + 3)/3]/[(-5 + 3)/3)] + C

= x^(-2/3)/(-2/3) + C

= -3/2x^(2/3) + C

**Question 10**

Integrate the following with respect to x ,(1/x³)^(1/4)

**Solution:**

(1/x³)^(1/4) = 1/x^3^(1/4)

= 1/x^(3/4)

= x^(-1)(3/4)

= x^(-3/4)

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 -3/4

So we get,

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

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

= x^(1/4)/(1/4) + C

= 4x^(1/4) + C

integration worksheet1 solution2 integration worksheet1 solution2

- Back to worksheet
- 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