Advertisements
Advertisements
प्रश्न
`intx^2 e^(x^3) dx` equals:
पर्याय
`1/3 e^(x^3) + C`
`1/3 e^(x^2) + C`
`1/2 e^(x^3) + C`
`1/2 e^(x^2) + C`
Advertisements
उत्तर
`1/3 e^(x^3) + C`
स्पष्टीकरण:
`int x^2 e^(x^3)` dx
Putting x3 = t, 3x2 dx = dt
`= 1/3 int (3x^2)e^(x^3)` dx
`= 1/3 int e^t dt = 1/3 e^t + C`
`= 1/3 e^(x^3) + C`
APPEARS IN
संबंधित प्रश्न
If u and v are two functions of x then prove that
`intuvdx=uintvdx-int[du/dxintvdx]dx`
Hence evaluate, `int xe^xdx`
Integrate the function in x sin x.
Integrate the function in x log 2x.
Integrate the function in x cos-1 x.
Integrate the function in `(xe^x)/(1+x)^2`.
Evaluate the following:
`int x tan^-1 x . dx`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Integrate the following w.r.t.x : log (x2 + 1)
`int ("x" + 1/"x")^3 "dx"` = ______
`int ("d"x)/(x - x^2)` = ______
Evaluate `int 1/(x(x - 1)) "d"x`
`int cot "x".log [log (sin "x")] "dx"` = ____________.
`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
`int1/(x+sqrt(x)) dx` = ______
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Evaluate:
`inte^x sinx dx`
The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.
Complete the following activity:
`int_0^2 dx/(4 + x - x^2) `
= `int_0^2 dx/(-x^2 + square + square)`
= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`
= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`
= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4) dx`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
Evaluate the following.
`intx^2e^(4x)dx`
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
Evaluate the following.
`intx^3/(sqrt(1 + x^4))dx`
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
If \(u\) and \(v\) are differentiable functions, which formula is used for integration by parts?
Let \[I=\int e^x\sin x\,dx.\] After applying integration by parts once, which equation is obtained?
