Question

please me....plz
∫(3+2x)^2dx
calculate the indefinite integral

Answer 1

Answer:

$\bold\red{9x + \frac{4}{3} {x}^{3} + 6 {x}^{2} + c}$

Step-by-step explanation:

We have to find the integration of,

$</p><p>\int {(3 + 2x)}^{2} dx$

After expanding the terms,

we get,

$\int(9 + 4 {x}^{2} + 12x)dx$

Now,

we know that,

$\int {x}^{n} = \frac{ {x}^{n + 1} }{n + 1}$

So,

according to this,

we get

Integration

$\bold{9x + \frac{4}{3} {x}^{3} + 6 {x}^{2} + c}$

where, c is an arbitrary constant

Answer 2

Answer:

4x³

9x + ------ + 6x² + c

3

Step-by-step explanation:

To find----->

------------

∫(3+2x)²dx

Solution----->

--------------

∫(3+2x)²dx

we have an identity as follows

(a+b)²= a²+ b²+ 2ab ,applying it here

= ∫{(3)² + (2x)² + 2 (3) (2x)} dx

= ∫(9 + 4x² + 12x ) dx

= ∫9 dx + ∫4x² dx + ∫ 12x dx

x^(n+1)

we have a formula ∫xⁿdx=-------------- + c

(n+1)

applying it

= 9∫ 1 dx + 4 ∫ x² dx + 12∫ x¹ dx

x³ x²

= 9 x + 4 ------ + 12 ------- + c

3 2

4x³

=9x + ------- + 6x² + c

3

Additional formulee---->

---------------------------------

1

1:∫----- dx = log x +c

x

aˣ

2: ∫aˣ dx= ----------- + c

log a

e

3: ∫eˣ dx = eˣ + c

4: ∫sinx dx = -cosx + c

5: ∫cosx dx = sinx +c

6: ∫sec²x dx = tan x +c

7: ∫secx tanx dx =sec x + c

8: ∫cosec² x=- cot x + c

9: ∫ cosecx cotx =-cosecx + c