Advertisements
Advertisements
Question
Solution
Let I= \[\int\]sin3 x . cos x dx
⇒ cos x dx = dt
\[ = \frac{\sin^4 x}{4} + C \left( \because t = \sin x \right)\]
APPEARS IN
RELATED QUESTIONS
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
cot x log sin x
Write a value of
Write a value of
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
Evaluate: `int "x" * "e"^"2x"` dx
`int 1/(cos x - sin x)` dx = _______________
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int (sin4x)/(cos 2x) "d"x`
`int cot^2x "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int (f^'(x))/(f(x))dx` = ______ + c.
`int(log(logx) + 1/(logx)^2)dx` = ______.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
