Advertisements
Advertisements
प्रश्न
Evaluate: `int "dx"/("9x"^2 - 25)`
Advertisements
उत्तर
Let I = `int "dx"/("9x"^2 - 25)`
`= int 1/(9 ("x"^2 - 25/9))` dx
`= 1/9 int 1/("x"^2 - (5/3)^2)` dx
`= 1/9 * 1/(2 * 5/3) log |("x" - 5/3)/("x" + 5/3)|` + c
∴ I = `1/30 log |(3"x" - 5)/("3x" + 5)|` + c
APPEARS IN
संबंधित प्रश्न
Prove that:
`int sqrt(x^2 - a^2)dx = x/2sqrt(x^2 - a^2) - a^2/2log|x + sqrt(x^2 - a^2)| + c`
Integrate the function in x sin 3x.
Integrate the function in x (log x)2.
Integrate the function in ex (sinx + cosx).
Prove that:
`int sqrt(x^2 + a^2)dx = x/2 sqrt(x^2 + a^2) + a^2/2 log |x + sqrt(x^2 + a^2)| + c`
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following : `int x^3.logx.dx`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
Choose the correct options from the given alternatives :
`int (x- sinx)/(1 - cosx)*dx` =
Integrate the following w.r.t.x : sec4x cosec2x
Evaluate the following.
`int x^3 e^(x^2)`dx
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "dx"/(5 - 16"x"^2)`
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
Evaluate:
∫ (log x)2 dx
`int (cos2x)/(sin^2x cos^2x) "d"x`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
Find: `int e^x.sin2xdx`
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
Prove that `int sqrt(x^2 - a^2)dx = x/2 sqrt(x^2 - a^2) - a^2/2 log(x + sqrt(x^2 - a^2)) + c`
Evaluate the following.
`intx^3 e^(x^2) dx`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate:
`int x^2 cos x dx`
`∫ sin^(−1)` xdx is equal to ______.
