Realizada con pythontex usando sympy y pandas Tabla de derivadas e integrales Función Derivada Integral f(x)=kf(x)=kf(x)=k f′(x)=0f'(x)=0f′(x)=0 ∫k dx=kx+C\int k\, dx=k x+C∫kdx=kx+C f(x)=xf(x)=xf(x)=x f′(x)=1f'(x)=1f′(x)=1 ∫x dx=x22+C\int x\, dx=\frac{x^{2}}{2}+C∫xdx=2x2+C f(x)=xnf(x)=x^{n}f(x)=xn f′(x)=nxnxf'(x)=\frac{n x^{n}}{x}f′(x)=xnxn ∫xn dx=xn+1n+1+C\int x^{n}\, dx=\frac{x^{n + 1}}{n + 1}+C∫xndx=n+1xn+1+C f(x)=1xf(x)=\frac{1}{x}f(x)=x1 f′(x)=−1x2f'(x)=- \frac{1}{x^{2}}f′(x)=−x21 ∫1x dx=ln(x)+C\int \frac{1}{x}\, dx=\ln{\left(x \right)}+C∫x1dx=ln(x)+C f(x)=xf(x)=\sqrt{x}f(x)=x f′(x)=12xf'(x)=\frac{1}{2 \sqrt{x}}f′(x)=2x1 - ∫x dx=2x323+C\int \sqrt{x}\, dx=\frac{2 x^{\frac{3}{2}}}{3}+C∫xdx=32x23+C f(x)=x1nf(x)=x^{\frac{1}{n}}f(x)=xn1 f′(x)=x1nnxf'(x)=\frac{x^{\frac{1}{n}}}{n x}f′(x)=nxxn1 ∫x1n dx=x1+1n1+1n+C\int x^{\frac{1}{n}}\, dx=\frac{x^{1 + \frac{1}{n}}}{1 + \frac{1}{n}}+C∫xn1dx=1+n1x1+n1+C f(x)=axf(x)=a^{x}f(x)=ax f′(x)=axln(a)f'(x)=a^{x} \ln{\left(a \right)}f′(x)=axln(a) ∫ax dx={axln(a)for ln(a)≠0xotherwise+C\int a^{x}\, dx=\begin{cases} \frac{a^{x}}{\ln{\left(a \right)}} & \text{for}\: \ln{\left(a \right)} \neq 0 \\x & \text{otherwise} \end{cases}+C∫axdx={ln(a)axxforln(a)=0otherwise+C f(x)=exf(x)=e^{x}f(x)=ex - f′(x)=exf'(x)=e^{x}f′(x)=ex - ∫ex dx=ex+C\int e^{x}\, dx=e^{x}+C∫exdx=ex+C f(x)=sin(x)f(x)=\sin{\left(x \right)}f(x)=sin(x) f′(x)=cos(x)f'(x)=\cos{\left(x \right)}f′(x)=cos(x) - ∫sin(x) dx=−cos(x)+C\int \sin{\left(x \right)}\, dx=- \cos{\left(x \right)}+C∫sin(x)dx=−cos(x)+C f(x)=cos(x)f(x)=\cos{\left(x \right)}f(x)=cos(x) f′(x)=−sin(x)f'(x)=- \sin{\left(x \right)}f′(x)=−sin(x) ∫cos(x) dx=sin(x)+C\int \cos{\left(x \right)}\, dx=\sin{\left(x \right)}+C∫cos(x)dx=sin(x)+C f(x)=tan(x)f(x)=\tan{\left(x \right)}f(x)=tan(x) f′(x)=tan2(x)+1f'(x)=\tan^{2}{\left(x \right)} + 1f′(x)=tan2(x)+1 ∫tan(x) dx=−ln(cos(x))+C\int \tan{\left(x \right)}\, dx=- \ln{\left(\cos{\left(x \right)} \right)}+C∫tan(x)dx=−ln(cos(x))+C f(x)=cot(x)f(x)=\cot{\left(x \right)}f(x)=cot(x) f′(x)=−cot2(x)−1f'(x)=- \cot^{2}{\left(x \right)} - 1f′(x)=−cot2(x)−1 ∫cot(x) dx=ln(sin(x))+C\int \cot{\left(x \right)}\, dx=\ln{\left(\sin{\left(x \right)} \right)}+C∫cot(x)dx=ln(sin(x))+C f(x)=1cos2(x)f(x)=\frac{1}{\cos^{2}{\left(x \right)}}f(x)=cos2(x)1 f′(x)=2sin(x)cos3(x)f'(x)=\frac{2 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}}f′(x)=cos3(x)2sin(x) ∫1cos2(x) dx=sin(x)cos(x)+C\int \frac{1}{\cos^{2}{\left(x \right)}}\, dx=\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}+C∫cos2(x)1dx=cos(x)sin(x)+C f(x)=1sin2(x)f(x)=\frac{1}{\sin^{2}{\left(x \right)}}f(x)=sin2(x)1 f′(x)=−2cos(x)sin3(x)f'(x)=- \frac{2 \cos{\left(x \right)}}{\sin^{3}{\left(x \right)}}f′(x)=−sin3(x)2cos(x) ∫1sin2(x) dx=−cos(x)sin(x)+C\int \frac{1}{\sin^{2}{\left(x \right)}}\, dx=- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}+C∫sin2(x)1dx=−sin(x)cos(x)+C f(x)=11−x2f(x)=\frac{1}{\sqrt{1 - x^{2}}}f(x)=1−x21 f′(x)=x(1−x2)32f'(x)=\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}}f′(x)=(1−x2)23x ∫11−x2 dx=asin(x)+C\int \frac{1}{\sqrt{1 - x^{2}}}\, dx=\operatorname{asin}{\left(x \right)}+C∫1−x21dx=asin(x)+C f(x)=1x2+1f(x)=\frac{1}{x^{2} + 1}f(x)=x2+11 f′(x)=−2x(x2+1)2f'(x)=- \frac{2 x}{\left(x^{2} + 1\right)^{2}}f′(x)=−(x2+1)22x ∫1x2+1 dx=atan(x)+C\int \frac{1}{x^{2} + 1}\, dx=\operatorname{atan}{\left(x \right)}+C∫x2+11dx=atan(x)+C f(x)=1a2+x2f(x)=\frac{1}{a^{2} + x^{2}}f(x)=a2+x21 f′(x)=−2x(a2+x2)2f'(x)=- \frac{2 x}{\left(a^{2} + x^{2}\right)^{2}}f′(x)=−(a2+x2)22x ∫1a2+x2 dx=atan(xa)a+C\int \frac{1}{a^{2} + x^{2}}\, dx=\frac{\operatorname{atan}{\left(\frac{x}{a} \right)}}{a}+C∫a2+x21dx=aatan(ax)+C