Question

Integrate the following functions :
1.
r3
I+x8
dx​

Answer 1

Answer:

Let I=∫

16x

8

−25

x

3

dx...(1)

Let u=x

4

∴du=4x

3

dx

∴x

3

dx=

4

du

or,I=

4

1

∫

16u

2

−25

du

or, I=

4

1

∫

(4u)

2

−(5)

2

du

[∵∫

x

2

−a

2

dx

=

2a

1

log

∣

∣

∣

∣

∣

x+a

x−a

∣

∣

∣

∣

∣

]+c

or, I=

4

1

×

2(5)

1

log

∣

∣

∣

∣

∣

4u+5

4u−5

∣

∣

∣

∣

∣

+c

∴=

4

1

log

∣

∣

∣

∣

∣

4x

4

+5

4x

4

−5

∣

∣

∣

∣

∣

+c

Ans (where c= constant of integration)

Step-by-step explanation:

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