Advertisements
Advertisements
Question
Integrate the function in ex (sinx + cosx).
Advertisements
Solution
Let `I = int e^x (sin x + cos x) dx`
Put ex sin x = t
`=> (e^x cos x + e^x sin x) dx = dt`
`therefore e^x (sin x + cos x) dx = dt`
`therefore I = int dt = t + C`
`= e^x sin x + C`
APPEARS IN
RELATED QUESTIONS
Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.
`intx^2 e^(x^3) dx` equals:
Prove that:
`int sqrt(x^2 + a^2)dx = x/2 sqrt(x^2 + a^2) + a^2/2 log |x + sqrt(x^2 + a^2)| + c`
Evaluate the following:
`int x tan^-1 x . dx`
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following: `int logx/x.dx`
Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
Choose the correct options from the given alternatives :
`int (1)/(x + x^5)*dx` = f(x) + c, then `int x^4/(x + x^5)*dx` =
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*dx` =
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Evaluate the following.
`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "dx"/(5 - 16"x"^2)`
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int(x + 1/x)^3 dx` = ______.
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
Evaluate `int(3x-2)/((x+1)^2(x+3)) dx`
`inte^(xloga).e^x dx` is ______
`int(xe^x)/((1+x)^2) dx` = ______
Evaluate:
`intcos^-1(sqrt(x))dx`
Evaluate:
`int (logx)^2 dx`
Prove that `int sqrt(x^2 - a^2)dx = x/2 sqrt(x^2 - a^2) - a^2/2 log(x + sqrt(x^2 - a^2)) + c`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate:
`int x^2 cos x dx`
Which function is an example under priority \(I\) in the LIATE rule?
Evaluate \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx.\]
Which substitution can also be used before integrating by parts for \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx?\]
Which differentiation identity verifies the special integral \[\int e^x\left[f(x)+f'(x)\right]dx=e^xf(x)+C?\]
