Question

this question is in trigonometric functions chapter

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Answer 1

Answer:

1/6 ( tan⁻¹ x³ )² + C

Step-by-step explanation:

Solution------> 1) Plz see the attachment

2) We solve it by substitution method , we put ,

tan⁻¹ ( x³ ) = t

Then we differentiate both sides , by using two formulee of differentiation , which are as follows ,

a) d/dx ( tan⁻¹ x ) = 1 / ( 1 + x² )

b) d/dx ( xⁿ ) = n xⁿ⁻¹

Applying it we get ,

x² dx / ( 1 + x⁶ ) = dt / 3

3) Putting it in original question , we get ,

1/3 ∫ t dt

4) We have a formula of intregation as follows ,

∫ xⁿ dx = xⁿ⁺¹ / ( n + 1 ) + C

Applying it we get , the answer

Additional information----->

1) ∫ 1 / x dx = logx + C

2) ∫ eˣ dx = eˣ + C

3) ∫ aˣ dx = aˣ / loga + C

4) ∫ Sinx dx = - Cosx + C

5) ∫ Cosx dx = Sinx + C

6) ∫ Sec² x dx = tanx + C

7) ∫ Secx tanx dx = Secx + C

8) ∫ Cosec²x dx = - Cot x + C

9) ∫ Cosecx Cotx dx = - Cosecx