Advertisements
Advertisements
प्रश्न
`int (x + 3)/(x + 4)^2 "e"^x "d"x` = ______.
Advertisements
उत्तर
`int (x + 3)/(x + 4)^2 "e"^x "d"x` = `"e"^x/(x + 4) + "C"`.
Explanation:
Let I = `int (x + 3)/(x + 4)^2 * "e"^x "d"x`
= `int (x + 4 - 1)/(x + 4)^2 * "e"^x "d"x`
= `int [(x + 4)/(x + 4)^2 - 1/(x + 4)^2]"e"^x "d"x`
= `int [1/(x + 4) - 1/(x + 4)^2]"e"^x "d"x`
Put `1/(x + 4)` = t
⇒ `- 1/(x + 4)^2 "d"x` = dt
Let f(x) = `1/(x + 4)`
∴ f'(x) = `- 1/(x + 4)^2`
Using `int "e"^x ["f"(x) + "f'"(x)]"d"x = "e"^x "f"(x) + "C"`
∴ I = `"e"^x * 1/(x + 4) + "C"`.
APPEARS IN
संबंधित प्रश्न
Evaluate the following definite integrals:
Evaluate the following integral:
Evaluate the following integral:
Evaluate each of the following integral:
If f (a + b − x) = f (x), then \[\int\limits_a^b\] x f (x) dx is equal to
Evaluate : \[\int e^{2x} \cdot \sin \left( 3x + 1 \right) dx\] .
\[\int\limits_0^1 \cos^{- 1} x dx\]
\[\int\limits_0^1 \left( \cos^{- 1} x \right)^2 dx\]
\[\int\limits_0^{\pi/2} \frac{1}{1 + \tan^3 x} dx\]
\[\int\limits_{- \pi}^\pi x^{10} \sin^7 x dx\]
\[\int\limits_0^{\pi/2} \frac{1}{2 \cos x + 4 \sin x} dx\]
\[\int\limits_0^2 \left( 2 x^2 + 3 \right) dx\]
\[\int\limits_{- 1}^1 e^{2x} dx\]
Evaluate the following using properties of definite integral:
`int_0^1 x/((1 - x)^(3/4)) "d"x`
Evaluate the following:
`int_0^oo "e"^(- x/2) x^5 "d"x`
If f(x) = `{{:(x^2"e"^(-2x)",", x ≥ 0),(0",", "otherwise"):}`, then evaluate `int_0^oo "f"(x) "d"x`
Choose the correct alternative:
Using the factorial representation of the gamma function, which of the following is the solution for the gamma function Γ(n) when n = 8 is
Choose the correct alternative:
`int_0^oo x^4"e"^-x "d"x` is
Given `int "e"^"x" (("x" - 1)/("x"^2)) "dx" = "e"^"x" "f"("x") + "c"`. Then f(x) satisfying the equation is:
