Advertisements
Advertisements
Question
Write a value of
Advertisements
Solution
Let I=\[\int\] ex (sin x + cos x) dx
⇒ (ex . sin x + ex cos x) dx = dt
\[\therefore I = \int dt\]
\[ = t + C\]
\[ = e^x \sin x + C \left( \because t = e^x \sin x \right)\]
APPEARS IN
RELATED QUESTIONS
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Evaluate: `int 1/(x(x-1)) dx`
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
`int logx/(log ex)^2*dx` = ______.
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
`int sqrt(1 + sin2x) dx`
`int cot^2x "d"x`
`int(log(logx))/x "d"x`
`int(1 - x)^(-2) dx` = ______.
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int sin^-1 x`dx = ?
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int (f^'(x))/(f(x))dx` = ______ + c.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
`int cos^3x dx` = ______.
Evaluate `int(1 + x + x^2 / (2!))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
