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integral mod(x)= 1/2(x 2 ).sgn(x)
Hi, I think there is some probl;em with the image u uploaded. Please upload the image again to get solution !
Factorise the denominator. Partial fractions and then integration by standard results.
Solve all these using integration by parts
I found a simpler way to solve this ,than integration by parts.
Hi, This is a Homogeneous differential equation. So put y=vx and solve, ie keeping v as avariable find dv/dx in terms of dy/dx and substitute also substitute the value of y in the expression. Upon...
I = ∫ (3x 3 -5x 2 +4x-9)dx / (x 2 +2) = ∫ (3x-5)dx + ∫ (-2x+1)dx / (x 2 +2) [Simple division] = 3x 2 /2 – 5x – ∫ 2xdx / (x 2 +2) + ∫ dx / (x 2 +2) = 3x 2 /2 – 5x – log|x 2 +2| + 1/rt(2)*tan -1...
log x 2 = 2 logx and integration of logx is =xlogx – x,,using ILATE so the answer is 2(xlogx -x)
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Split a 3 -x 3 = (a-x)(a 2 +ax+x 2 ) then use partial fraction method to convert into simple form and by the method of substitution, integrate.
let the above exp be I . also using prop of int . I=integration of 1/1-cosx addinging both I’s 2I=integration of (1/1+cosx + 1/1-cosx) simplify 2I=integration of (2cosec^2 x.) hope it helps
resolve into (a-x)(a^2+x^2+ax) ,then use partial fractions.
(sin 7 x.cos 3x )/10 + 3/7*sin 7/ 10
Consider dx/dy dx/dy = (e 2x –y 2 )/y 3 Put e x =t gives, e x dx/dy = dt/dy So, dt/dy = t 3 /y 3 – t/y Now, let t=vy so, dt/dy = v+ydv/dy gives, v+ydv/dy=v 3 -v therefore, ∫dv/(v 3 -2v) =...