Advertisements
Advertisements
प्रश्न
Evaluate `int (3"a"x)/("b"^2 + "c"^2x^2) "d"x`
Advertisements
उत्तर
Let v = b2 + c2x2, then dv = 2c2 xdx
Therefore, `int (3"a"x)/("b"^2 + "c"^2x^2) "d"x`
= `(3"a")/(2"c"^2) int "dv"/"v"`
= `(3"a")/("c"^2) log |"b"^2 + "c"^2x^2| + "C"`
APPEARS IN
संबंधित प्रश्न
\[\int\limits_0^{( \pi )^{2/3}} \sqrt{x} \cos^2 x^{3/2} dx\]
Evaluate the following integral:
Evaluate the following integral:
Solve each of the following integral:
If \[\int\limits_0^1 \left( 3 x^2 + 2x + k \right) dx = 0,\] find the value of k.
Evaluate :
\[\int\limits_0^{\pi/2} \frac{1}{2 + \cos x} dx\] equals
The value of the integral \[\int\limits_{- 2}^2 \left| 1 - x^2 \right| dx\] is ________ .
\[\int\limits_0^{\pi/2} \frac{\sin x}{\sqrt{1 + \cos x}} dx\]
\[\int\limits_0^\pi \sin^3 x\left( 1 + 2 \cos x \right) \left( 1 + \cos x \right)^2 dx\]
\[\int\limits_0^\infty \frac{x}{\left( 1 + x \right)\left( 1 + x^2 \right)} dx\]
\[\int\limits_0^{\pi/2} x^2 \cos 2x dx\]
\[\int\limits_1^3 \left| x^2 - 4 \right| dx\]
\[\int\limits_0^{\pi/2} \frac{1}{1 + \cot^7 x} dx\]
\[\int\limits_{\pi/6}^{\pi/2} \frac{\ cosec x \cot x}{1 + {cosec}^2 x} dx\]
\[\int\limits_1^3 \left( x^2 + 3x \right) dx\]
Evaluate the following:
`int_1^4` f(x) dx where f(x) = `{{:(4x + 3",", 1 ≤ x ≤ 2),(3x + 5",", 2 < x ≤ 4):}`
Evaluate the following using properties of definite integral:
`int_0^1 log (1/x - 1) "d"x`
Integrate `((2"a")/sqrt(x) - "b"/x^2 + 3"c"root(3)(x^2))` w.r.t. x
`int x^9/(4x^2 + 1)^6 "d"x` is equal to ______.
`int x^3/(x + 1)` is equal to ______.
Find: `int logx/(1 + log x)^2 dx`
