# Integrals

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Integration by substitution

Integration by parts

Some various integrals

• The integral of sin(x)cos(x) dx, $\int {\sin x\cos x\;dx}$
• The integral of 1/sqrt(1-x^2) dx, $\int {\frac{{dx}}{{\sqrt {1 - {x^2}} }}}$
• The integral of one over sqrt(x^2+1) dx, $\int {\frac{{dx}}{{\sqrt {{x^2} + 1} }}}$
• The integral of sqrt(1-x^2) dx, $\int {\sqrt {1 - {x^2}} \,dx}$
• The integral of sqrt(x^2-1) dx, $\int {\sqrt {{x^2}-1} \,dx}$
• The integral of sqrt(x^2+1) dx, $\int {\sqrt {{x^2} + 1} \,dx}$

A rather peculiar rule

Some special integrals

• The integral $\int\limits_0^\infty {\frac{{{e^{ - px}} - {e^{ - qx}}}}{x}dx}$
• The integral $\int\limits_{ - \infty }^\infty {\frac{{\sin x}}{x}dx}$
• The integral $\int\limits_0^1 {\frac{{\ln (x + 1)}}{{{x^2} + 1}}dx}$
• The integral $\int\limits_{ - \infty }^\infty {{e^{ - {x^2}}}dx}$
• The integral $\int\limits_{ - \infty }^\infty {{e^{ - {x^2}}}dx}$, a second way. Up a level : Calculus and Analysis
Previous page : The hyperbolic functions
Next page : Differential Equations Last modified: May 18, 2019 @ 12:59