Advertisements
Advertisements
प्रश्न
Find:
`int_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`
Advertisements
उत्तर
Let
` "I" = int_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`
` "I" = int_(-pi/4)^0 (1+sin"x"/cos"x")/(1-sin"x"/cos"x")"dx"`
` "I" = int_(-pi/4)^0 (cos"x"+sin"x")/(cos"x"-sin"x")"dx"`
Let
cos x - sin x = t
- (sin x + cos x) dx = dt
For x `=(-pi)/4,"t" = sqrt2` and x = 0, t = 1
`"I" = -int_(sqrt2)^1 "dt"/"t"`
`"I" = int_1^sqrt2 "dt"/"t"`
` = ["lnt"]_1^sqrt2`
` = "ln"sqrt2`
APPEARS IN
संबंधित प्रश्न
Find:
`int(x^3-1)/(x^3+x)dx`
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `1/sqrt((2-x)^2 + 1)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `x^2/sqrt(x^6 + a^6)`
Integrate the function `(x + 2)/sqrt(x^2 -1)`
Integrate the function `(x+2)/sqrt(x^2 + 2x + 3)`
Integrate the function `(x + 3)/(x^2 - 2x - 5)`
`int dx/(x^2 + 2x + 2)` equals:
Integrate the function:
`sqrt(x^2 + 4x + 6)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
Integrate the function:
`sqrt(x^2 + 3x)`
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
Evaluate \[\int \frac{dx}{x^2-a^2}\].
Evaluate \[\int \frac{dx}{x^2+a^2}\].
Evaluate \[\int \frac{dx}{\sqrt{x^2-a^2}}\].
Evaluate \[\int \frac{dx}{\sqrt{x^2+a^2}}\].
Evaluate \[\int\frac{dx}{x^2-6x+13}\].
What is the completed-square form of \[3x^2+13x-10\]?
Which is the correct split for \[\int\frac{x+2}{2x^2+6x+5}\,dx\]?
