Advertisements
Advertisements
प्रश्न
`intx^2 e^(x^3) dx` equals:
विकल्प
`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
Integrate the function in x log x.
Integrate the function in `e^x (1 + sin x)/(1+cos x)`.
Evaluate the following:
`int x^2 sin 3x dx`
Evaluate the following : `int x.cos^3x.dx`
Evaluate the following:
`int x.sin 2x. cos 5x.dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
Integrate the following functions w.r.t.x:
`e^(5x).[(5x.logx + 1)/x]`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Choose the correct options from the given alternatives :
`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =
Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
`int 1/sqrt(2x^2 - 5) "d"x`
Choose the correct alternative:
`int ("d"x)/((x - 8)(x + 7))` =
`int(x + 1/x)^3 dx` = ______.
`int"e"^(4x - 3) "d"x` = ______ + c
Evaluate `int 1/(x(x - 1)) "d"x`
`int logx/(1 + logx)^2 "d"x`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.
`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
`int(1-x)^-2 dx` = ______
`intsqrt(1+x) dx` = ______
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
The integrating factor of `ylogy.dx/dy+x-logy=0` is ______.
`int logx dx = x(1+logx)+c`
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate:
`inte^x sinx dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate:
`int1/(x^2 + 25)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
