Advertisements
Advertisements
प्रश्न
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Advertisements
उत्तर
Let I= \[\int\] cos4 x .sin x dx
⇒ –sin x dx = dt
⇒ sin x dx = –dt
\[= \frac{- t^5}{5} + C\]
\[ = - \frac{\cos^5 x}{5} + C \left( \because t = \cos x \right)\]
APPEARS IN
संबंधित प्रश्न
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int (sin4x)/(cos 2x) "d"x`
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int (cos x)/(1 - sin x) "dx" =` ______.
`int ("d"x)/(x(x^4 + 1))` = ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int1/(x(x - 1))dx`
Which standard substitution is used for \[\sqrt{x^2+\mathrm{a}^2}\], \[\frac{1}{\sqrt{x^2+\mathrm{a}^2}}\], or \[x^2+\mathrm{a}^2\]?
After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?
For \[\int\frac{\sin x}{\sin(x+a)}\,dx\], which substitution gives \[dx=dt\]?
How should a substitution be chosen?
