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Popular Calculus Problems

integral of-cos(x)ln(x)	\int\:-\cos(x)\ln(x)dx
integral of x/(sqrt((36-x^2)^3))	\int\:\frac{x}{\sqrt{(36-x^{2})^{3}}}dx
limit as x approaches infinity of 1+x^2	\lim\:_{x\to\:\infty\:}(1+x^{2})
(e^{sin(x)})^'	(e^{\sin(x)})^{\prime\:}
integral from 1 to 4 of e^x	\int\:_{1}^{4}e^{x}dx
derivative of y=(x^2+1)^5(1-x^2)^5	derivative\:y=(x^{2}+1)^{5}(1-x^{2})^{5}
derivative of f(x)=x^3-2x^2+5	derivative\:f(x)=x^{3}-2x^{2}+5
derivative of f(x)=3x^3+6x^2+7x	derivative\:f(x)=3x^{3}+6x^{2}+7x
integral of (2x^4+x^2-x-2)/(x^3(x+1))	\int\:\frac{2x^{4}+x^{2}-x-2}{x^{3}(x+1)}dx
integral of 2xsin(x)	\int\:2x\sin(x)dx
y^'+8y=t+e^{-7t}	y^{\prime\:}+8y=t+e^{-7t}
derivative of 5x^3-6cos(x)	derivative\:5x^{3}-6\cos(x)
tangent of f(x)= 2/(x-8),(10,1)	tangent\:f(x)=\frac{2}{x-8},(10,1)
integral of csc^2(2x)	\int\:\csc^{2}(2x)dx
integral of 8/(x^2)	\int\:\frac{8}{x^{2}}dx
taylor e^{2x-3},1	taylor\:e^{2x-3},1
limit as x approaches 2 of 5x^3-6x-1	\lim\:_{x\to\:2}(5x^{3}-6x-1)
integral of (x^{-2/7})	\int\:(x^{-\frac{2}{7}})dx
implicit (dy)/(dx),y=x^5+8	implicit\:\frac{dy}{dx},y=x^{5}+8
limit as x approaches-1 of 2x+3	\lim\:_{x\to\:-1}(2x+3)
integral from-pi to pi of cos(2x)cos(nx)	\int\:_{-π}^{π}\cos(2x)\cos(nx)dx
integral of x/(x^2-5)	\int\:\frac{x}{x^{2}-5}dx
derivative of 7^{x^4+x}	derivative\:7^{x^{4}+x}
integral of (sin(t)sqrt(1+cos(t)))	\int\:(\sin(t)\sqrt{1+\cos(t)})dt
tangent of y=3x-2sqrt(x),(1,1)	tangent\:y=3x-2\sqrt{x},(1,1)
(2e^y-x)(dy)/(dx)=1	(2e^{y}-x)\frac{dy}{dx}=1
derivative of (7+x^5)	\frac{d}{dx}((7+x)^{5})
limit as x approaches-0 of ln(x)	\lim\:_{x\to\:-0}(\ln(x))
derivative of y=(x^2+32sqrt(x))/8 ,x=4	derivative\:y=\frac{x^{2}+32\sqrt{x}}{8},x=4
inverse oflaplace 2/(s^3(s^2-9))	inverselaplace\:\frac{2}{s^{3}(s^{2}-9)}
(d^2)/(dx^2)(3sqrt(x)-8/x)	\frac{d^{2}}{dx^{2}}(3\sqrt{x}-\frac{8}{x})
limit as x approaches 4+of (x-4)/(\|x-4\|)	\lim\:_{x\to\:4+}(\frac{x-4}{\left\|x-4\right\|})
limit as x approaches 0 of (sin^2(x))/x	\lim\:_{x\to\:0}(\frac{\sin^{2}(x)}{x})
derivative of ln((\|x-1\|/(\|x-3\|)))	\frac{d}{dx}(\ln(\frac{\left\|x-1\right\|}{\left\|x-3\right\|}))
integral of 2xsec^2(3x)x	\int\:2x\sec^{2}(3x)xdx
limit as x approaches 1+of (4x)/(2x-2)	\lim\:_{x\to\:1+}(\frac{4x}{2x-2})
limit as x approaches 0 of g(x)sin(1/x)	\lim\:_{x\to\:0}(g(x)\sin(\frac{1}{x}))
derivative of sec(xtan(x))	\frac{d}{dx}(\sec(x)\tan(x))
(\partial)/(\partial x)(2yln(x))	\frac{\partial\:}{\partial\:x}(2y\ln(x))
derivative of 10^{sin(pix})	\frac{d}{dx}(10^{\sin(πx)})
integral of x/(sqrt(16-9x^2))	\int\:\frac{x}{\sqrt{16-9x^{2}}}dx
integral of 4x^3e^{-x^2}	\int\:4x^{3}e^{-x^{2}}dx
derivative of (-x+sqrt(1+x)/(x^2-1))	\frac{d}{dx}(\frac{-x+\sqrt{1+x}}{x^{2}-1})
integral of sin^3(x)cos^{18}(x)	\int\:\sin^{3}(x)\cos^{18}(x)dx
derivative of ((x^3+y^3)/((x^2+y^2)))	\frac{d}{dx}(\frac{(x^{3}+y^{3})}{(x^{2}+y^{2})})
derivative of (x+2/2)	\frac{d}{dx}(\frac{x+2}{2})
49y^{''}+70y^'+25y=0	49y^{\prime\:\prime\:}+70y^{\prime\:}+25y=0
integral of 4tan(3x)	\int\:4\tan(3x)dx
sum from n=1 to infinity of sin(1/((n)))	\sum\:_{n=1}^{\infty\:}\sin(\frac{1}{(n)})
derivative of 4(x^3-x^4)	\frac{d}{dx}(4(x^{3}-x)^{4})
integral from 0 to 1 of-2x5^x	\int\:_{0}^{1}-2x5^{x}dx
3x^2y^2dx+ydy=5xy	3x^{2}y^{2}dx+ydy=5xy
integral from 1 to 9 of 1/x	\int\:_{1}^{9}\frac{1}{x}dx
integral of (sqrt(x^2-4))	\int\:(\sqrt{x^{2}-4})dx
tangent of f(x)=x^3-2x+2,(3,23)	tangent\:f(x)=x^{3}-2x+2,(3,23)
integral from 0 to x^3 of (t+1)(t-2)	\int\:_{0}^{x^{3}}(t+1)(t-2)dt
derivative of (x^4+2x-1/(5x^2-2x+1))	\frac{d}{dx}(\frac{x^{4}+2x-1}{5x^{2}-2x+1})
integral of (x^2)/(sqrt(x^2+4))	\int\:\frac{x^{2}}{\sqrt{x^{2}+4}}dx
(\partial)/(\partial x)(xy^3-x)	\frac{\partial\:}{\partial\:x}(xy^{3}-x)
integral of 1/(sqrt(324-x^2))	\int\:\frac{1}{\sqrt{324-x^{2}}}dx
integral of tan^8(7x)sec^4(7x)	\int\:\tan^{8}(7x)\sec^{4}(7x)dx
tangent of f(x)=x^2-1,\at x=-3	tangent\:f(x)=x^{2}-1,\at\:x=-3
(\partial)/(\partial x)(3yx^2)	\frac{\partial\:}{\partial\:x}(3yx^{2})
derivative of 5-8x	\frac{d}{dx}(5-8x)
(\partial}{\partial y}(-\frac{y^3)/3-8x)	\frac{\partial\:}{\partial\:y}(-\frac{y^{3}}{3}-8x)
limit as n approaches infinity of n/(sqrt(10+n))	\lim\:_{n\to\:\infty\:}(\frac{n}{\sqrt{10+n}})
inverse oflaplace ((s+2)^2)/(s^3)	inverselaplace\:\frac{(s+2)^{2}}{s^{3}}
limit as x approaches 3 of (x-3)/(x^2+9)	\lim\:_{x\to\:3}(\frac{x-3}{x^{2}+9})
limit as x approaches 0 of x-2	\lim\:_{x\to\:0}(x-2)
integral of (x+5)/(x^2+4x+3)	\int\:\frac{x+5}{x^{2}+4x+3}dx
limit as x approaches-8 of x+6	\lim\:_{x\to\:-8}(x+6)
integral of (7ln(x+8))/(x^2)	\int\:\frac{7\ln(x+8)}{x^{2}}dx
(dy)/(dx)-2xy=10,y(0)=-8	\frac{dy}{dx}-2xy=10,y(0)=-8
integral from 2 to 4 of 4(3x-1)	\int\:_{2}^{4}4(3x-1)dx
y^{''}-100y=0	y^{\prime\:\prime\:}-100y=0
derivative of 1/(x^2-3x+2)	\frac{d}{dx}(\frac{1}{x^{2}-3x+2})
4y^'-12x^2=0	4y^{\prime\:}-12x^{2}=0
(\partial)/(\partial x)(xsin^2(xy-y))	\frac{\partial\:}{\partial\:x}(x\sin^{2}(xy-y))
integral of 3/(4x)	\int\:\frac{3}{4x}dx
derivative of x^2-4x+2	derivative\:x^{2}-4x+2
sum from n=0 to infinity of 1/(n(n-1))	\sum\:_{n=0}^{\infty\:}\frac{1}{n(n-1)}
derivative of 1/(2sqrt(r))+1/(7r^{6/7)}	derivative\:\frac{1}{2\sqrt{r}}+\frac{1}{7r^{\frac{6}{7}}}
f(x)=(x^2+11x+24)/(x+8)	f(x)=\frac{x^{2}+11x+24}{x+8}
(dx)/(dt)=sqrt(x)	\frac{dx}{dt}=\sqrt{x}
(ln(x-1))^'	(\ln(x-1))^{\prime\:}
tangent of y= x/((1+x^2))	tangent\:y=\frac{x}{(1+x^{2})}
integral from-infinity to 3 of 1/(4+x^2)	\int\:_{-\infty\:}^{3}\frac{1}{4+x^{2}}dx
derivative of f(x)=e^{9x}+9e^{9x}x	derivative\:f(x)=e^{9x}+9e^{9x}x
derivative of x^3+xe^y-2y	\frac{d}{dx}(x^{3}+xe^{y}-2y)
integral of 1/((x^2+4)^2)	\int\:\frac{1}{(x^{2}+4)^{2}}dx
integral of 6x(-x^2+5)^7	\int\:6x(-x^{2}+5)^{7}dx
x^2-3xy+x(dy)/(dx)=0	x^{2}-3xy+x\frac{dy}{dx}=0
limit as x approaches 2 of (2-x)/(x-2)	\lim\:_{x\to\:2}(\frac{2-x}{x-2})
f(x)=-4cos(2x)	f(x)=-4\cos(2x)
(\partial)/(\partial x)(5x-6y+z)	\frac{\partial\:}{\partial\:x}(5x-6y+z)
integral of ln(1-sqrt(x))	\int\:\ln(1-\sqrt{x})dx
derivative of y=arccot(sqrt(2t))	derivative\:y=\arccot(\sqrt{2t})
integral of (4x^2)/((16+x^2)^2)	\int\:\frac{4x^{2}}{(16+x^{2})^{2}}dx
y^{''}-6y^'-7y=15e^{2t}	y^{\prime\:\prime\:}-6y^{\prime\:}-7y=15e^{2t}
integral of-5/(x^2)	\int\:-\frac{5}{x^{2}}dx

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