Advertisements
Advertisements
प्रश्न
`int x^9/(4x^2 + 1)^6 "d"x` is equal to ______.
विकल्प
`1/(5x)(4 + 1/x^2)^-5 + "C"`
`1/5(4 + 1/x^2)^-5 + "C"`
`1/(10x)(1 + 4)^-5 + "C"`
`1/10(1/x^2 + 4)^-5 + "C"`
Advertisements
उत्तर
`int x^9/(4x^2 + 1)^6 "d"x` is equal to `1/10(1/x^2 + 4)^-5 + "C"`.
Explanation:
Let I = `int x^9/(4x^2 + 1)^6 "d"x`
= `int x^9/(x^12(4 + 1/x^2)^6) "d"x`
= `int 1/(x^3(4 + 1/x^2)^6) "d"x`
Put `(4 + 1/x^2)` = t
⇒ `(-2)/x^3 "dt"` = dt
⇒ `"dx"/x^3 = - 1/2 "dt"`
∴ I = `- 1/2 int "dt"/"t"^6`
= `- 1/2 xx - 1/5 "t"^-5 + "C"`
= `1/10 "t"^-5 + "C"`
= `1/10(4 + 1/x^2)^-5 + "C"`
APPEARS IN
संबंधित प्रश्न
Evaluate the following definite integrals:
If f(2a − x) = −f(x), prove that
Evaluate each of the following integral:
\[\int\limits_0^1 \left\{ x \right\} dx,\] where {x} denotes the fractional part of x.
If \[\left[ \cdot \right] and \left\{ \cdot \right\}\] denote respectively the greatest integer and fractional part functions respectively, evaluate the following integrals:
The value of the integral \[\int\limits_0^{\pi/2} \frac{\sqrt{\cos x}}{\sqrt{\cos x} + \sqrt{\sin x}} dx\] is
\[\int\limits_0^\infty \frac{1}{1 + e^x} dx\] equals
If \[\int\limits_0^1 f\left( x \right) dx = 1, \int\limits_0^1 xf\left( x \right) dx = a, \int\limits_0^1 x^2 f\left( x \right) dx = a^2 , then \int\limits_0^1 \left( a - x \right)^2 f\left( x \right) dx\] equals
The value of \[\int\limits_0^{\pi/2} \log\left( \frac{4 + 3 \sin x}{4 + 3 \cos x} \right) dx\] is
Evaluate : \[\int\limits_0^{2\pi} \cos^5 x dx\] .
Evaluate : \[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\] .
\[\int\limits_0^{\pi/2} \frac{\sin x}{\sqrt{1 + \cos x}} dx\]
\[\int\limits_1^2 \frac{x + 3}{x\left( x + 2 \right)} dx\]
\[\int\limits_2^3 \frac{\sqrt{x}}{\sqrt{5 - x} + \sqrt{x}} dx\]
Using second fundamental theorem, evaluate the following:
`int_0^(pi/2) sqrt(1 + cos x) "d"x`
Evaluate the following:
f(x) = `{{:("c"x",", 0 < x < 1),(0",", "otherwise"):}` Find 'c" if `int_0^1 "f"(x) "d"x` = 2
Evaluate the following using properties of definite integral:
`int_(-1)^1 log ((2 - x)/(2 + x)) "d"x`
Evaluate the following:
`int_0^oo "e"^(- x/2) x^5 "d"x`
Evaluate the following integrals as the limit of the sum:
`int_0^1 x^2 "d"x`
`int x^3/(x + 1)` is equal to ______.
