Integration Techniques (Substitution, Parts, Partial Fractions): JEE Questions & Solutions

If ( x)^- 112 ( x)^- 52 dx is equal to - p1q1( x)^ 92 - p2q2( x)^ 52 - p3q3( x)^ 12 + p4q4( x)^- 32 + C, where pi, qi are positive integers…

Let for f(x) = 7 ^8 x + 7 ^6 x - 3 ^4 x - 3 ^2 x, I1 = 0^ 4 f(x)dx and I2 = 0^ 4 x f(x)dx. Then 7I1 + 12I2 is equal to:

Let I(x) = dx(x-11)^ 1113 (x+15)^ 1513. If I(37) - I(24) = 14 ( 1b^1/13 - 1c^1/13), where b, c N, then 3(b+c) is equal to:

Let x^3 x dx = g(x) + C, where C is the constant of integration. If g ( 2) + g ( 2) = ^3 + ^2 +,,, Z, then + - equals:

Let f(x) = x^3 3-x^2 dx. If 5f( 2) = -4, then f(1) is equal to

If ( 1x + 1x^3) ( [23]3x^-24 + x^-26) dx is equal to - 3( + 1) ( 3x^ + x^)^ + 1 + C, x 0, where,, Z and C is the constant of integration,…

Let f(x) be a positive function and I1 = - 12^1 2x f (2x(1-2x)) dx and I2 = -1^2 f (x(1-x)) dx. Then the value of I2I1 is equal to

Evaluate the integral 1^0 1 3 + x + 1 + x dx in the form a + b 2 + c 3; find 2a + 3b - 4c.

The value of (2 + 3 x) x (1 + x) dx is equal to:

Let I(x) = x^2(x ^2 x + x)(x x + 1)^2 dx. If I(0) = 0, then I ( 4) is equal to:

Let I(x) = 0^x x+1x(1+x e^x)^2 dx, x 0. If x I(x) = 0, then I(1) is equal to:

Let f(x)= dx(3+4x^2) 4-3x^2, |x|< 2 3. If f(0)=0 and f(1)= 1 ^-1 (),, 0, then ^2+ ^2 is equal to