44++ Common Integral Table

Common Integral Table. Z 1 1+x2 dx =. Z tanxdx= ln cosx +c 7.

Constant multiple rule [ ]cu cu dx d = ′, where c is a constant. N6= 1 (2) z 1 x dx= lnjxj (3) z udv= uv z vdu (4) z 1 ax+ b dx= 1 a lnjax+ bj integrals of rational functions (5) z 1 (x+ a)2 dx= 1 x+ a (6) z (x+ a)ndx= (x+ a)n+1 n+ 1;n6= 1 (7) z x(x+ a)ndx= (x+ a)n+1((n+ 1)x a) (n+ 1)(n+ 2) (8) z 1 1 + x2 dx= tan 1 x (9) z 1 a2 + x2 dx= 1 a tan 1 x a 1 Table of integrals ∗ basic forms z xndx = 1 n +1 xn+1 (1) z 1 x dx =ln|x| (2) z udv = uv z vdu (3) z 1 ax + b dx = 1 a ln|ax + b| (4) integrals of rational functions z 1 (x + a)2 dx = 1 x + a (5) z (x +.

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Z e xdx= e +c 4. Finding antiderivatives and indefinite integrals: Table of integrals∗ basic forms z xndx = 1 n+ 1 xn+1 (1) z 1 x dx= lnjxj (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= ln(1 x+ a (5) z (x+. This is the currently selected item.

You need to recognize when to use the substitution u = kx, for constant k. ∫ 𝑥 𝑥2+1 =arctan(𝑥) ∫ 𝑥 √1−𝑥2 =arcsin(𝑥) ∫ −1 √1−𝑥2 𝑥=arccos(𝑥) ∫ −1 𝑥2+1 𝑥=arccot(𝑥) Integration — is one of the main mathematical operations. Udv a b ∫=#uv$% a b −vdu a b ∫ u and v are functions of x. Here is a.

Z f(x)g0(x)dx = f(x)g(x) z g(x)f0(x)dx integrals of rational and irrational functions 3. Z tanxdx= ln cosx +c 7. Z 1 x2 dx = 1 x +c 9. Table 2.1, choose yp in the same line and determine its undetermined coefficients by substituting yp and its derivatives into (4). Z cosec2 xdx= cotx+c 11.

Sum and difference rule [ ]u v u v dx d ± = ±′ 3. An+1 0 ∞ ∫ integration by parts: Z f (g(x))g0(x)dx = z f(u)du integration by parts 2. Z cdx = cx+c 6. Table of useful integrals, etc.

Table of integrals ∗ basic forms z xndx = 1 n +1 xn+1 (1) z 1 x dx =ln|x| (2) z udv = uv z vdu (3) z 1 ax + b dx = 1 a ln|ax + b| (4) integrals of rational functions z 1 (x + a)2 dx = 1 x + a (5) z (x +. Z.