Find the antiderivative of the following function.
$f\(\left\)(x\(\right\))=5x^4$

Checking Antiderivative Formulas

Right, or wrong? Say which for each formula and give a brief reason for each answer.

∫√(2x + 1) dx = √(x² + x +C)

Checking Antiderivative Formulas

Right, or wrong? Give a brief reason why.

∫−15(x + 3)² / (x − 2)⁴ dx = ((x + 3)/(x − 2))³ + C

Finding Antiderivatives

In Exercises 1–16, find an antiderivative for each function. Do as many as you can mentally. Check your answers by differentiation.

−πsin πx

Find the antiderivative of the following function.

$f\(\left\)(x\(\right\))=200$

Find the antiderivative of the following function.

$f\(\left\)(x\(\right\))=10x^9$

For the following function $f\(\left\)(x\(\right\))$, find the antiderivative $F\(\left\)(x\(\right\))$ that satisfies the given condition.

$f\(\left\)(x\(\right\))=5x^4$; $F\(\left\)(0\(\right\))=1$

For the following function $f\(\left\)(x\(\right\))$, find the antiderivative $F\(\left\)(x\(\right\))$ that satisfies the given condition.

$f\(\left\)(x\(\right\))=100x^{99}$; $F\(\left\)(1\(\right\))=101$

Find all functions whose derivative is f'(x) = x + 1.