Find the most general antiderivative for each of the following functions?

Question

a) f(x) = x(x^2 + 1)^10
b) f(x) = 3x +1 / 3x^2 + 2x - 4
c) f(x) = sin^2 x (read as "sine sqaured x", not "sine to the 2x")
d) f(x) = cosxe^sinx + 3x^(4/5)
e) f(x) = tanx
f) f(x) = 1/(x^2 + 4)

Answer 1

Nagpapatawa ba kayo?

a) [ (x^2 + 1) ^ 11 ] / 22 + C
b) [ In | 3x^2 + 2x - 4 | ] / 2 + C
c) x / 2 - (sin 2x) / 4 + C
d) e^sin x + 5x^(9/5) / 3 + C
e) In |sec x| + C
f) [arctan (x/2)] / 2 + C

Answer 2

First improve this function f(x) = x (7 - x) ^2 f(x) = x( 7^2 - 2*7x + (-x)^2 ) f(x) = x( x^2 - 14x + 40 9) f(x) = x^3 - 14 x^2 + 40 9 x Then discover the antiderivative.... F(x) = x^4 / 4 - 14 * x^3 / 3 + 40 9 x^2 / 2 + C F(x) = a million/4 * x^4 - 14/3 * x^3 + 40 9/2 *x^2 + C

Answer 3

Hehehe. It looks as if at least one person (Joe) didn't sleep through Calculus


Doug