Q1 ∫ ^{e ^{log e √x}}⁄_xdx

Solution

Q2 9^log₃xdx

Solution

Q3 ∫ e^{3log x (x⁴)}dx

Solution

Q4 ∫√ (1-sin 2x)dx

Solution

Q5 ∫ ^{sin x + cos x}⁄_{√

(1 + sin 2x)}

Solution

Q6 ∫ ^{cos x - cos 2x}⁄_{1 - cos x}

Solution

Q7 ∫ (e^{x loga} + e ^{a logx} - e^{a loga})dx

Solution

Q8 ∫ ^2x⁄_{(2x + 1)²}dx

Solution

Q9 ∫ (3x + 1)√ 2x - 1dx

Solution

Q10 ∫ ^{x + 2}⁄_{√

3x + 1} dx

Solution

Q11 ∫ sin 7x sin x dx

Solution

Q12 ∫ (sin⁶x + cos⁶x)dx

Solution

Q13 ∫ ^{1 + cos 4x}⁄_{cot x - tan x}dx

Solution

Q14 ∫ ^{6x² + 1}⁄_{(4x³ + 2x - 5)³}dx

Solution

Q15 ∫ ^{1 + cotx}⁄_{x + log sin x} dx

Solution

Q16 ∫ ^dx⁄_{x cos² (1 + log x)}

Solution

Q17 ∫ e^-x cosec² (2e^-x + 5)dx

Solution

Q18 ∫ ^{e^x(1+x)}⁄_cos²(xe^x)dx

Solution

Q19 ∫ ^{cosec x}⁄_{log (tan ^x⁄₂)} dx

Solution

Q20 ∫ ^{sin 2x}⁄_{(a + b cos x)²}dx

Solution

Q21 ∫ cot x log sin x dx

Solution

Q22 ∫ sec x log | sec x + tan x| dx

Solution

Q23 ∫ ^cos⁵x⁄_{sin x}

Solution

Q24 ∫ cos³x e ^{log sin x}dx

Solution

Q25 ∫ cosec⁶ x dx

Solution

Q26 ∫ tan ⁸ x sec ⁴ x dx

Solution

Q27 ∫ ^dx⁄_{√

sin³ x sin (x + ∝)} dx

Solution

Q28 ∫ ^{sin x - x cos x}⁄_{x (x + sin x)} dx

Solution

Q29 ∫ ^dx⁄_{√x + ∛x}

Solution

Q30 ∫ ^{(x⁴ - x)^1/4}⁄_x⁵ dx

Solution

Q31 If f’(x) = a sinx + b cos x, f’(0) = 4, f(0) = 4, f(0) =3 and f(π/2)=5, find f(x).

Solution

Q32 Find the anti derivatives of the following functions:^{(x+1)(x+logx)}⁄_2x

Solution

Q33 Find the anti derivatives of the following functions:^{3(cos^-1x)²}⁄_{√

1-x²}

Solution

Q34 Find all the primitives of the following functions:^x-2⁄_{2x²-8x 5} dx

Solution

Q35 Find all the primitives of the following functions:^cosec²x⁄_{2 + 3 cot
x} dx

Solution

Q36 Find all the primitives of the following functions:^{x -1}⁄_{x (x - log x)}

Solution