In this page integration worksheet2 solution8 we are going to see
solution of some practice question from the worksheet of integration.

**Question 8**

(i) Integrate the following with respect to x ,e^(3x)

**Solution:**

The given question exactly matches the formula

**∫ **** e^(a x) = (1/a) e^ (a x) + C**

Now we are going to integrate the given question by using this formula,in the question instead of "a" we have 3

So we get,

∫e^(3 x) dx = (1/3) e ^(3 x) + C

(ii) Integrate the following with respect to x ,e^(x + 3)

**Solution:**

The given question exactly matches the formula

**∫ **** e^(a x + b) = (1/a) e^ (a x + b) + C**

Now we are going to integrate the given question by using this formula,in the question instead of "a" we have 1

So we get,

∫e^(x + 3) dx = (1/1) e ^(x + 3) + C

= e ^(x + 3) + C

(iii) Integrate the following with respect to x , e^(3 x + 2)

**Solution:**

The given question exactly matches the formula

**∫ **** e^(a x + b) = (1/a) e^ (a x + b) + C**

Now we are going to integrate the given question by using this formula,in the question instead of "a" we have 3

So we get,

∫ e^(3 x + 2)) dx = (1/3) e ^(3 x + 2) + C

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

(iv) Integrate the following with respect to x ,e^(5 - 4 x)

**Solution:**

The given question exactly matches the formula

**∫ **** e^(a x + b) = (1/a) e^ (a x + b) + C**

Now we are going to integrate the given question by using this formula,in the question instead of "a" we have -4

So we get,

∫e^(5 - 4 x) dx = (1/-4) e ^(5 - 4 x) + C

= -e ^(x + 3)/4 + C

(v) Integrate the following with respect to x ,e^(a x + b)

**Solution:**

The given question exactly matches the formula

**∫ **** e^(a x + b) = (1/a) e^ (a x + b) + C**

Now we are going to integrate the given question by using this formula,in the question instead of "a" we have a

So we get,

∫e^(a x + b) dx = (1/a) e ^(a x + b) + C

integration worksheet2 solution8 integration worksheet2 solution8

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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