Advertisements
Advertisements
प्रश्न
Integrate the function `(3x)/(1+ 2x^4)`
Advertisements
उत्तर
Let `I = int (3x)/ (1 + 2x^4) dx`
Put x2 = t
⇒ 2x dx = dt
⇒ `x dx = dt/2`
∴ `I = 3/2 int dt/(1 + 2t^2 )`
`= 3/4 int dt/ (1/2 + t^2)`
`= 3/4 int dt/ ((1/sqrt2)^2 + t^2)` `....[∵ int dx/(a^2+x^2) = 1/a tan^-1 x/a + C]`
`3/4* 1/ (1/sqrt2) tan^-1 (t/(1/sqrt2)) + C`
`3/(2sqrt2) tan^-1 sqrt2t + C`
APPEARS IN
संबंधित प्रश्न
Evaluate: `int(5x-2)/(1+2x+3x^2)dx`
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `1/sqrt(9 - 25x^2)`
Integrate the function `x^2/sqrt(x^6 + a^6)`
Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`
Integrate the function `1/sqrt(8+3x - x^2)`
Integrate the function `(x + 2)/sqrt(x^2 -1)`
Integrate the function `(6x + 7)/sqrt((x - 5)(x - 4))`
Integrate the function `(x + 3)/(x^2 - 2x - 5)`
Integrate the function:
`sqrt(x^2 + 4x + 6)`
Integrate the function:
`sqrt(x^2 + 4x +1)`
Integrate the function:
`sqrt(1+ x^2/9)`
`int sqrt(1+ x^2) dx` is equal to ______.
Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
Find: `int (dx)/(x^2 - 6x + 13)`
What is a standard integral?
Evaluate \[\int \frac{dx}{x^2-a^2}\].
Evaluate \[\int \frac{dx}{a^2-x^2}\].
Evaluate \[\int \frac{dx}{x^2+a^2}\].
Evaluate \[\int \frac{dx}{\sqrt{x^2-a^2}}\].
For \[\int\frac{px+q}{ax^2+bx+c}\,dx\], how is \[px+q\] written in relation to the derivative of the denominator?
Which statement is correct when integrating an expression that is not immediately a standard integral?
