Advertisements
Advertisements
प्रश्न
Verify the following:
`int (2x + 3)/(x^2 + 3x) "d"x = log|x^2 + 3x| + "C"`
Advertisements
उत्तर
L.H.S. = `int (2x + 3)/(x^2 + 3x) "d"x`
Put x2 + 3x = t
∴ (2x + 3) dx = dt
⇒ `int "dt"/"t" = log |"t"|`
⇒ `log |x^2 + 3x| + "C"` = R.H.S.
L.H.S. = R.H.S.
Hence verified.
APPEARS IN
संबंधित प्रश्न
Evaluate the following integral:
If `f` is an integrable function such that f(2a − x) = f(x), then prove that
\[\int\limits_0^{\pi/2} \frac{1}{2 + \cos x} dx\] equals
The value of \[\int\limits_{- \pi}^\pi \sin^3 x \cos^2 x\ dx\] is
The value of \[\int\limits_{- \pi/2}^{\pi/2} \left( x^3 + x \cos x + \tan^5 x + 1 \right) dx, \] is
\[\int\limits_0^{\pi/2} \frac{\sin^2 x}{\left( 1 + \cos x \right)^2} dx\]
\[\int\limits_1^2 \frac{1}{x^2} e^{- 1/x} dx\]
\[\int\limits_1^3 \left( 2 x^2 + 5x \right) dx\]
Choose the correct alternative:
`int_0^oo x^4"e"^-x "d"x` is
Integrate `((2"a")/sqrt(x) - "b"/x^2 + 3"c"root(3)(x^2))` w.r.t. x
Evaluate `int sqrt((1 + x)/(1 - x)) "d"x`, x ≠1
Evaluate `int "dx"/sqrt((x - alpha)(beta - x)), beta > alpha`
If `int (3"e"^x - 5"e"^-x)/(4"e"6x + 5"e"^-x)"d"x` = ax + b log |4ex + 5e –x| + C, then ______.
If x = `int_0^y "dt"/sqrt(1 + 9"t"^2)` and `("d"^2y)/("d"x^2)` = ay, then a equal to ______.
Evaluate: `int_(-1)^2 |x^3 - 3x^2 + 2x|dx`
