Question

help me in integration plss urgent hai​

Answer 1

To find -----> ∫ ( 2√x + 3/x⁴ ) dx

Solution----->

∫ ( 2 √x + 3/x⁴ ) dx

= ∫ 2 √x dx + ∫ 3 / x⁴ dx

= 2 ∫ √x dx + 3 ∫ dx / x⁴

= 2 ∫ x¹/² dx + 3 ∫ x⁻⁴ dx

= 2 x¹/² ⁺¹ / ( 1/2 + 1 ) + 3 x⁻⁴⁺¹ / ( -4 + 1 ) + C

= 2 x³/² / ( 3/2 ) + 3x⁻³ / ( - 3 ) + C

= 4/3 ( x³/² ) - x⁻³ + C

Additional information ----->

1) ∫ xⁿ dx = xⁿ⁺¹ / ( n + 1 ) + C

2) ∫ 1 / x dx = logx + C

3) ∫ eˣ dx = eˣ + C

4) ∫ aˣ dx = aˣ / loga + C

5) ∫ Sinx dx = - Cosx + C

6) ∫ Cosx dx = Sinx + C

7) ∫ Sec²x = tanx + C

8) ∫ Secx tanx dx = Secx + C

9) ∫ Cosecx Cotx dx = - Cosecx + C

10 ) ∫ Cosec²x dx = - Cotx + C