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Free antiderivative calculator - solve integrals with all the steps. Type in any integral to get the solution, steps and graph.
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The Integral Calculator lets you calculate integrals and antiderivatives of functions online — for free! Our calculator allows you to check your solutions to calculus exercises. It helps you practice by showing you the full working (step by step integration).
10 Νοε 2020 · \[\dfrac{d}{dx}(\sin x)=\cos x, \nonumber\] so \(F(x)=\sin x\) is an antiderivative of \(\cos x\). Therefore, every antiderivative of \(\cos x\) is of the form \(\sin x+C\) for some constant \(C\) and every function of the form \(\sin x+C\) is an antiderivative of \(\cos x\). d. Since \[\dfrac{d}{dx}(e^x)=e^x, \nonumber\] then \(F(x)=e^x\) is ...
25 Νοε 2023 · Find \(f(t)\), given that \(f''(t) = \cos t\), \(f'(0) = 3\) and \(f(0) = 5\). Solution. We start by finding \(f'(t)\), which is an antiderivative of \(f''(t)\): \[ \int f''(t)\ dt = \int \cos t\ dt = \sin t + C = f'(t).\] So \(f'(t) = \sin t+C\) for the correct value of \(C\). We are given that \(f'(0) = 3\), so:
with functions like x3; p;exp;log;sin;cos;tan and arcsin;arccos;arctan. Example: The function f(x) = sin(sin(ˇ+ p x+ x2)) + log(1 + exp((x6 + 1)=(x2 + 1)) + (arctan(ex))1=3 is an elementary function. Example: The anti derivative of the sinc function is called the sine-integral Si(x) = Z x 0 sin(t) t dt: The function Si(x) is not an elementary ...
1 Find the anti-derivative of f(x) = sin(4x) + 20x3 + 1/x. Solution: We can take the anti-derivative of each term separately. The antiderivative is F(x) = −cos(4x)/4 + 4x4 + log(x)+C. 2 Find the anti derivative of f(x) = 1/cos2(x)+1/(1− x). Solution: we can find the anti derivatives of each term separately and add them up.
In essence we are asking Dx£?§ = 2x. Because Dx£x2§ = 2x, the function x2 is an antiderivative of 2x. Dx£x2 + C§ = 2x. Thus the function f (x) = 2x has infinitely many antiderivatives F(x) = x2 + C. Their graphs are the graph of y = x2 raised (or lowed) by C units. Figure 38.1. The antiderivatives of the function f (x) = 2x.
