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If the first term is 7x^5, ∫7x^5 -cox dx is the expression. You can split this up into two integrals if that helps you visualize the terms. ∫7x^5dx - ∫cox dx. We know that the antiderivative of cosx is sinx, so that is our second term. In the first term, we must undo the power rule, adding one to the power and multiplying by the reciprocal of the power. This gives us (7/6)x^6. So, our final antiderivative expression is
(7/6)x^6-sinx+C, with C being an arbitrary constant.
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What is the antiderivative of e to the -x?
-e-x + C.
How can you calculate the arbitrary constant in the solution to an antiderivative?
You can't, unless it's an initial value problem. If f(x) is an antiderivative to g(x), then so is f(x) + c, for any c at all.
What is the antiderivative of x to the 43?
If f' (x) = x43, then f(x) = (1/44) x44 + C.
What is the antiderivative of xex?
One can use integration by parts to solve this. The answer is (x-1)e^x.
What is the anti derivative of the square root of 1-x2?
-1
