Question

integrate tan^5 x sec^2 x dx​

Answer 1

Answer:

tan⁶x / 6 + C

Step-by-step explanation:

To find ---> ∫ tan⁵x Sec²x dx

Solution--->

I =∫ tan⁵x Sec²x dx

= ∫ ( tanx )⁵ Sec²x dx

Let , tanx = t

Differentiating both sides we get,

=> Sec²x dx = dt

I = ∫ ( t )⁵ dt

= ∫ t⁵ dt

We have a formula ∫ xⁿ dx = xⁿ⁺¹ / ( n + 1 ) + C , applying it here we get,

= t⁵⁺¹ / ( 5 + 1 ) + C

= t⁶ / 6 + C

Putting t = tanx , we get,

I = tan⁶x / 6 + C

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) ∫ Secx tanx dx = Secx + C

7) ∫ Sec²x dx = tanx + C

8) ∫ Cosec²x dx = - Cotx + C

9) ∫ Cosecx Cotx dx = - Cosecx + C

Answer 2

Step-by-step explanation:

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