Easy calc 1 question?

Easy calc 1 question?

Whats the anti derivative of 7x

∫ (7x) dx

First factor out the coefficient out of the integrand: ∫ a f(x) = a ∫ f(x)...so...

7 ∫(x) dx

Now to find anti-derivative of 'x'....we simply apply the power rule for which we take the exponent...add one to the exponent and then the new exponent becomes the new denominator: x^b = (x^(b+1))/(b+1))..so we have...

7 ∫(x^(1+1))/(1+1)

7 * (x^2)/2 + c

(7x^2)/2 + c <--- answer (where 'c' is some arbitrary constant)...or as..

(7/2)x^2 + c

7/2x^2

the " antiderivative " of A x^k is A x^(k+1) / [ k + 1 ]

its alot

(7x^2)/2 + C