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 sin−1 x.
Integrate the function in (sin-1x)2.
Integrate the function in e2x sin x.
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following : `int x^2*cos^-1 x*dx`
Integrate the following functions w.r.t. x : `sqrt(5x^2 + 3)`
Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`
Integrate the following functions w.r.t. x : `((1 + sin x)/(1 + cos x)).e^x`
Integrate the following functions w.r.t. x : `log(1 + x)^((1 + x)`
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Evaluate the following.
`int x^2 e^4x`dx
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Choose the correct alternative from the following.
`int (1 - "x")^(-2) "dx"` =
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
`int 1/(4x + 5x^(-11)) "d"x`
`int (cos2x)/(sin^2x cos^2x) "d"x`
∫ log x · (log x + 2) dx = ?
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
Evaluate the following:
`int_0^pi x log sin x "d"x`
`int tan^-1 sqrt(x) "d"x` is equal to ______.
If u and v ore differentiable functions of x. then prove that:
`int uv dx = u intv dx - int [(du)/(d) intv dx]dx`
Hence evaluate `intlog x dx`
Find: `int e^x.sin2xdx`
Solve: `int sqrt(4x^2 + 5)dx`
If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
`int1/sqrt(x^2 - a^2) dx` = ______
Evaluate:
`intcos^-1(sqrt(x))dx`
Evaluate:
`inte^x sinx dx`
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`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
Evaluate the following.
`intx^3/(sqrt(1 + x^4))dx`
