Question

Q 1.
Find [5x* dx
Oa) 20x3 + c
Ob) 5x5 + c
Oc) 5x3 + c
Od) x5 + c​

Answer 1

Answer:

X5+c...................

Answer 2

Answer:

ANSWER

Consider the given integral.

I=∫5

5

5

x

⋅5

5

x

⋅5

x

dx

Let, u=5

5

x

⇒x=

ln5

ln5

lnu

du=5

x+5

x

ln

2

(5)dx

dx=

(ln5)

2

5

−x−5

x

du

Thus, we have,

I=∫5

u

u5

x

(ln5)

2

5

−x−5

x

du

I=∫

(ln5)

2

u5

u−5

ln5

ln5

lnu

du

I=

(ln5)

2

1

∫5

u

du

I=

(ln5)

2

1

ln(5)

5

u

+C

I=

(ln(5))

3

1

+C

I=

(ln(5))

3

5

5

5

x

+C

Hence, this is the required result.