Advertisements
Advertisements
प्रश्न
`int x^3/(x + 1)` is equal to ______.
पर्याय
`x + x^2/2 + x^3/3 - log|1 - x| + "C"`
`x + x^2/2 - x^3/3 - log|1 - x| + "C"`
`x - x^2/2 - x^3/3 - log|1 + x| + "C"`
`x - x^2/2 + x^3/3 - log|1 + x| + "C"`
Advertisements
उत्तर
`int x^3/(x + 1)` is equal to `x - x^2/2 + x^3/3 - log|1 + x| + "C"`.
Explanation:
I = `int x^3/(x + 1)`
= `int (x^3 + 1 - 1)/(x + 1) "d"x`
= `int (x^3 + 1)/(x + 1) "d"x - int 1/(x + 1) "d"x`
= `int (x^2 - x + 1)"d"x - int 1/(x + 1) "d"x`
= `x^3/3 - x^2/2 + x - log|x + 1| + "C"`
APPEARS IN
संबंधित प्रश्न
If f is an integrable function, show that
If \[f\left( x \right) = \int_0^x t\sin tdt\], the write the value of \[f'\left( x \right)\]
If \[\int_0^a \frac{1}{4 + x^2}dx = \frac{\pi}{8}\] , find the value of a.
\[\int\limits_0^1 \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) dx\]
\[\int\limits_0^\infty \frac{x}{\left( 1 + x \right)\left( 1 + x^2 \right)} dx\]
\[\int\limits_0^a \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a - x}} dx\]
\[\int\limits_0^\pi x \sin x \cos^4 x dx\]
\[\int\limits_0^{\pi/2} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x} dx\]
Using second fundamental theorem, evaluate the following:
`int_0^3 ("e"^x "d"x)/(1 + "e"^x)`
Using second fundamental theorem, evaluate the following:
`int_1^2 (x - 1)/x^2 "d"x`
Evaluate the following using properties of definite integral:
`int_0^(i/2) (sin^7x)/(sin^7x + cos^7x) "d"x`
Evaluate the following:
`Γ (9/2)`
Evaluate the following:
`int_0^oo "e"^(-4x) x^4 "d"x`
If f(x) = `{{:(x^2"e"^(-2x)",", x ≥ 0),(0",", "otherwise"):}`, then evaluate `int_0^oo "f"(x) "d"x`
Evaluate the following:
`int ((x^2 + 2))/(x + 1) "d"x`
If `intx^3/sqrt(1 + x^2) "d"x = "a"(1 + x^2)^(3/2) + "b"sqrt(1 + x^2) + "C"`, then ______.
What is the meaning of an indefinite integral?
