Advertisements
Advertisements
Question
`intx^2 e^(x^3) dx` equals:
Options
`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
Solution
`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
RELATED QUESTIONS
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in `(xe^x)/(1+x)^2`.
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following : `int x.cos^3x.dx`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`
Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*dx` =
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Choose the correct options from the given alternatives :
`int (x- sinx)/(1 - cosx)*dx` =
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.
Choose the correct options from the given alternatives :
`int sin (log x)*dx` =
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 : `(3 - 2sinx)/(cos^2x)`
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Integrate the following w.r.t.x : sec4x cosec2x
Evaluate the following.
`int "e"^"x" "x"/("x + 1")^2` dx
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
`int 1/sqrt(2x^2 - 5) "d"x`
`int(x + 1/x)^3 dx` = ______.
Evaluate `int 1/(x log x) "d"x`
∫ log x · (log x + 2) dx = ?
`int cot "x".log [log (sin "x")] "dx"` = ____________.
`int log x * [log ("e"x)]^-2` dx = ?
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
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.
`int(logx)^2dx` equals ______.
If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
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 ______.
Solution of the equation `xdy/dx=y log y` is ______
Evaluate the following.
`int x^3 e^(x^2) dx`
`int(xe^x)/((1+x)^2) dx` = ______
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following:
`intx^3e^(x^2)dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate `int (1 + x + x^2/(2!))dx`
