Questions

Solution

Integrate the following with respect to x

(1)  x⁵ (1 + x⁶)⁷

(2)  (2Lx + m)/(Lx² + mx + n)

(3)  (4ax + 2b)/(ax² + bx + c)^10

Solution

(4)   x/√(x² + 3)

(5)  (2 x + 3) √(x² + 3 x - 5)

(6)  tan x

(7)  sec x

Solution

(8)  cos^14 x sin x

(9)  sin^5 x

(10) cos^7x

Solution

(11) (1 + tan x)/(x + log sec x)

(12)  e^m tan⁻¹x/(1+x²)

(13)  x sin⁻¹ (x²)/√(1 - x⁴)

(14)  5 (x + 1) (x + log x)⁴/x

Solution

(15)  sin (log x)/x

(16)  cot x/log sin x

(17)  sec⁴xtan x

(18)  tan³x sec x

(19) sin x/sin (x + a)

Solution

(20)  cos x/cos (x - a)

(21) √tan x/sin x cos x

(22) (log x)²/x

(23) e^(3 log x) e^x⁴

Solution

(24)  sin 2x/(a cos²x + b sin²x)

(25)  (1 - tan x)/(1 + tan x)

(26) x (L - x)^16

Solution

(27) x (x - a)^m

(28) x² (2 - x)^15

(29) sin√x/√x

Solution

(30) (x + 1)√(2 x + 3)

(31) (3 x + 5)√(2 x + 1)

(32) (x² + 1)√(x + 1)

Solution