Advertisements
Advertisements
प्रश्न
Integrate the functions:
sec2(7 – 4x)
उत्तर
Let `I = int sec^2` (7 - 4x) dx
Put 7 - 4x = t
- 4 dx = dt or dx `= - 1/4` dt
Hence, `I = - 1/4 int sec^2` t dt
`= - 1/4` tan t + C
`= - 1/4` tan (7 - 4x) + C
APPEARS IN
संबंधित प्रश्न
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Integrate the following functions w.r.t. x : `(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int1/(4 + 3cos^2x)dx` = ______
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following
`int x^3 e^(x^2) ` dx