Integral Table Pdf : Pdf Integral Table Lanonym Raouf Academia Edu / Table of standard integrals 1.. Z secxdx= ln secx+tanx +c 12. A bx x2 22 a sin and cos 1 sin2 2 b − ⇒= θ θθ −= 22 2 sec and tan sec 12 2 a. Z dx x = lnjxj+c 3. Z cotxdx= ln sinx +c 8. Table of standard integrals 1.

Dwight, tables of integrals and other mathematical data (1964) ? the most comprehensive tabulation of integrals is provided by: E−ax2dx= 1 2 π a # $% & '(1 2 0 ∞ ∫ ax xe−2dx= 1 2a 0 ∞ ∫ x2e−ax2dx= 1 4a π a # $% & '(1 2 0 ∞ ∫ x3e−ax2dx= 1 2a2 0 ∞ ∫ x2ne−ax2dx= 1⋅3⋅5⋅⋅⋅(2n−1) 2n+1an π a $ %& ' 1 2 0 ∞ ∫ x2n+1e−ax2dx= n! U inverse trig function (sin ,arccos , 1 xxetc) logarithmic functions (log3 ,ln( 1),xx etc) algebraic functions (xx x3,5,1/, etc) trig functions (sin(5 ),tan( ),xxetc) A limited but very useful table of integrals is: Table of integrals of reverse trigonometric functions the first member of each equation contains the function to be integrated, the second member contains the expanded integral.

Z secxdx=lnjsecx+tanxj+ c z cf(x)dx= c z f(x)dx z (f(x)+g(x))dx=z

Table of useful integrals, etc. Z secxdx= ln secx+tanx +c 12. Table of integrals basic forms z xndx= 1 n+ 1 xn+1 (1) z 1 x dx= lnx (2) z udv= uv z vdu (3) z 1 ax+ b dx= 1 a lnjax+ bj (4) integrals of rational functions z 1 (x+ a)2 dx= 1 x+ a (5) z (x+ a)ndx= (x+ a)n+1 n+ 1 + c;n6= 1 (6) z x(x+ a)ndx= (x+ a)n+1((n+ 1)x a) (n+ 1)(n+ 2) (7) z 1 1 + x2 dx= tan 1 x (8) z 1 a2 + x2 dx= 1 a tan 1 x a (9) z x a 2. Table of laplace transforms f(t) lf(t) = f(s) 1 1 s (1) eatf(t) f(s a) (2) u(t a) e as s (3) f(t a)u(t a) e asf(s) (4) (t) 1 (5) (t stt 0) e 0 (6) tnf(t) ( 1)n dnf(s) dsn (7) f0(t) sf(s) f(0) (8) fn(t) snf(s) s(n 1)f(0) (fn 1)(0) (9) z t 0 f(x)g(t x)dx f(s)g(s) (10) tn (n= 0;1;2;:::) n! Table of integrals of reverse trigonometric functions the first member of each equation contains the function to be integrated, the second member contains the expanded integral. Integration is the basic operation in integral calculus.while differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful. Decomposition according to the following table. Z secxdx=lnjsecx+tanxj+ c z cf(x)dx= c z f(x)dx z (f(x)+g(x))dx=z A short summary of this paper. The substitution u gx= ( )will convert (( )) ( ) ( ) ( ) b gb( ) a ga ∫∫f g x g x dx f u du= using du g x dx= ′( ). Z dx a 2+x = 1 a tan 1 x a +c 9. 23 ( ) 2 1. 2an+1 0 ∞ ∫ xne−axdx= n!

Table of useful integrals, etc. Z cosecxdx= ln cosecx cotx +c 13. Integral and derivative table in this table, a is a constant, while u, v, w are functions. Z secxdx= ln secx+tanx +c 12. Decomposition according to the following table.

Z cotxdx= ln sinx +c 8.

Integral and derivative table in this table, a is a constant, while u, v, w are functions. Table of laplace transforms f(t) lf(t) = f(s) 1 1 s (1) eatf(t) f(s a) (2) u(t a) e as s (3) f(t a)u(t a) e asf(s) (4) (t) 1 (5) (t stt 0) e 0 (6) tnf(t) ( 1)n dnf(s) dsn (7) f0(t) sf(s) f(0) (8) fn(t) snf(s) s(n 1)f(0) (fn 1)(0) (9) z t 0 f(x)g(t x)dx f(s)g(s) (10) tn (n= 0;1;2;:::) n! Table of standard integrals 1. Csun, integrals, table of integrals, math 280, math 351, differential equations created date: Table 2.1, choose yp in the same line and determine its undetermined coefficients by substituting yp and its derivatives into (4). The substitution u gx= ( )will convert (( )) ( ) ( ) ( ) b gb( ) a ga ∫∫f g x g x dx f u du= using du g x dx= ′( ). Z tanxdx= ln cosx +c 7. Table of integrals basic forms z xndx= 1 n+ 1 xn+1 (1) z 1 x dx= lnx (2) z udv= uv z vdu (3) z 1 ax+ b dx= 1 a lnjax+ bj (4) integrals of rational functions z 1 (x+ a)2 dx= 1 x+ a (5) z (x+ a)ndx= (x+ a)n+1 n+ 1 + c;n6= 1 (6) z x(x+ a)ndx= (x+ a)n+1((n+ 1)x a) (n+ 1)(n+ 2) (7) z 1 1 + x2 dx= tan 1 x (8) z 1 a2 + x2 dx= 1 a tan 1 x a (9) z x a 2. Dwight, tables of integrals and other mathematical data (1964) ? the most comprehensive tabulation of integrals is provided by: F(x) and g(x) are any continuous functions; Integrals with trigonometric functions z sinaxdx= 1 a cosax (63) z the gaussian integral 3 4. A limited but very useful table of integrals is: List of integrals of exponential functions 2 where where and is the gamma function when , , and when , , and definite integrals for, which is the logarithmic mean (the gaussian integral) (see integral of a gaussian function) (!!

Csun, integrals, table of integrals, math 280, math 351, differential equations created date: This leaflet provides such a table. Table of useful integrals, etc. 2an+1 0 ∞ ∫ xne−axdx= n! If a term in your choice for yp happens to be a solution of the homogeneous ode corresponding to (4), multiply this term by x (or by x 2 if this solution corresponds to a double root of the

Table of standard integrals 1.

Z dx x = lnjxj+c 3. Table of integrals engineers usually refer to a table of integrals when performing calculations involving integration. Table of standard integrals 1. 2an+1 0 ∞ ∫ xne−axdx= n! Decomposition according to the following table. U = u(x) is differentiable function of x; These restrictions are shown in the third column. For indefinite integrals drop the limits of integration. Sometimes restrictions need to be placed on the values of some of the variables. Integral of elliptic type to an r function by means of the integral formulas of table 1. A table of normal integrals. Integration is the basic operation in integral calculus.while differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful. Table of laplace transforms f(t) lf(t) = f(s) 1 1 s (1) eatf(t) f(s a) (2) u(t a) e as s (3) f(t a)u(t a) e asf(s) (4) (t) 1 (5) (t stt 0) e 0 (6) tnf(t) ( 1)n dnf(s) dsn (7) f0(t) sf(s) f(0) (8) fn(t) snf(s) s(n 1)f(0) (fn 1)(0) (9) z t 0 f(x)g(t x)dx f(s)g(s) (10) tn (n= 0;1;2;:::) n!