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Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform.. \int \frac{x}{x^2+1}dx. en. Related Symbolab blog posts. My Notebook, the Symbolab way.. It is one of the Standard Integral : ∫ 1 1 + x2 = arctanx + C. Aliter : Let, I = ∫ 1 1 +x2 dx. Subst. x = tanu. ∴ dx = sec2udu,&,u = arctanx. ∴ I = ∫ 1 1 +tan2u sec2udu, = ∫ 1 sec2u sec2udu, = ∫1du, = u. ⇒ I = arctanx + C.