NettetCalculus. Evaluate the Integral integral of 2/ (x^2-1) with respect to x. ∫ 2 x2 - 1dx. Since 2 is constant with respect to x, move 2 out of the integral. 2∫ 1 x2 - 1dx. Write the fraction … NettetSolve: ∫ x 4+x 2+1x dx A tan −1( 32x 2+ 31)+c B 3tan −1( 32x 2+ 31)+c C 31tan −1( 32x 2+ 31)+c D 3tan −1( 32x 2− 31)+c Hard Solution Verified by Toppr Correct option is C) Consider, I= x 4+x 2+1x dx put x 2+1=t⇒x 2=t−1⇒x 4=(t−1) 2 2xdx=dt xdx= 21dt. ⇒I=∫ 2[(t−1) 2+t]1 dt. = 21∫ t 2+1−2t+t1 dt = 21∫ t 2+1−t1 dt = 21∫ t 2+ 41−t+1− 411 dt

How do you integrate #x( (x^2) +1 )^ (1/2)#? - Socratic.org

NettetResolving x(x 2+1)1 into partial fractions x(x 2+1)1 = xA+ (x 2+1)Bx+C .... (1) 1=(A+B)x 2+ 1=(A+B)x 2+Cx+A On comparing, we get A=1,C=0,B=−1 Put these values in (1), we get x(x 2+1)1 = x1+ (x 2+1)−x Integrating both sides, we get ∫x(x 2+1)dx =∫ xdx−∫(x 2+1)xdx ⇒∫x(x 2+1)dx =logx− 21log∣1+x 2∣+c ∫x(x 2+1)dx =− 21log( x 2x 2+1)+c Nettet2 Answers. $$ \int \frac {x^2 -1} {x^2 + 1} dx = \int \frac {x^2 +1 - 1 - 1} {x^2+1}dx = \int dx - 2 \int\frac {dx} {x^2+1} = x - 2 \arctan x + C $$. Ick. I used to HATE problems like this in … person living abroad for good briefly

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Nettet16. mar. 2024 · Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo. NettetDerivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin … NettetCalculus Help: Integral ∫ (x^2+2x-1)/ (2x^3+3x^2-2x) dx - Integration by partial fractions Technique. Calculus Physics Chem Accounting Tam Mai Thanh Cao. 1K views 11 … stand up paddle board repair kit