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- Pennsylvania State University - All Campuses
- Mathematics
- Mathematics 251
- Xue
- Diff & Int

M G.

(a*u(x)+b*v(x))

a*u'+b*v

(u(x)*v(x))

u'*v+u*v

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(u(x)/v(x))

(u'*v-u*v')/v^2

x^n

n*x^(n-1)

e^x

e^x

log(x)

1/x

sin(x)

cos(x)

cos(x)

-sin(x)

tan(x)

(sin(x)/cos(x))'

=1/cos^2(x)

=1/cos^2(x)

S a*u(x)+b*v(x) dx

a*U+b*V+c

S u(x)*v' dx

uv- S u'*v(x) dx

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S f[g(x)]*g' dx

S f(y) dy

S x^n dx

x^(n+1)/(n+1) +c

S 1/x dx

log(x) +c

S e^x dx

e^x +c

S sin(x) dx

-cos(x) +c

S cos(x) dx

sin(x) +c

S tan(x) dx

S -(cos(x)'/cos(x)) dx

=-log|cos(x)| +c

=-log|cos(x)| +c

S x^n e^x dx

n!

=1*2*3*...*n

=1*2*3*...*n

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