Advertisements
Advertisements
Question
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Advertisements
Solution
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
RELATED QUESTIONS
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`1/(1 + cot x)`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate `int(3x^2 - 5)^2 "d"x`
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Write `int cotx dx`.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate:
`int sin^3x cos^3x dx`
