Advertisements
Advertisements
प्रश्न
Evaluate `int (3"x"^2 - 5)^2` dx
Advertisements
उत्तर
Let I = `int (3"x"^2 - 5)^2` dx
`= int (9"x"^4 - 30"x"^2 + 25)` dx
`= 9 int "x"^4 "dx" - 30 int "x"^2 "dx" + 25 int "dx"`
`= 9 ("x"^5/5) - 30 ("x"^3/3)` + 25x + c
∴ I = `9/5 "x"^5 - 10"x"^3 + 25"x" + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Write a value of
Write a value of\[\int \log_e x\ dx\].
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate: `int 1/(sqrt("x") + "x")` dx
`int 1/(cos x - sin x)` dx = _______________
`int x^2/sqrt(1 - x^6)` dx = ________________
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int (log x)/(log ex)^2` dx = _________
`int logx/x "d"x`
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int(1 + x + x^2 / (2!))dx`
