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Popular Calculus Problems

integral of e^t	\int\:e^{t}dt
derivative of (1+x^5)	\frac{d}{dx}((1+x)^{5})
integral of (tan^2(3x))/(csc(3x))	\int\:\frac{\tan^{2}(3x)}{\csc(3x)}dx
integral of [(sqrt(x)+3)/(5sqrt(x))]	\int\:[\frac{\sqrt{x}+3}{5\sqrt{x}}]dx
integral of ((e^x))/((e^x-1)(e^x+3))	\int\:\frac{(e^{x})}{(e^{x}-1)(e^{x}+3)}dx
y^'=(pi*x+y+pi^2)^2	y^{\prime\:}=(π\cdot\:x+y+π^{2})^{2}
integral of ln(3x^2)	\int\:\ln(3x^{2})dx
integral of sin^4(b)	\int\:\sin^{4}(b)
derivative of 12xe^x	derivative\:12xe^{x}
integral of sqrt((x^2-7)/(x^8))	\int\:\sqrt{\frac{x^{2}-7}{x^{8}}}dx
limit as x approaches 0+of x^2ln(x^2)	\lim\:_{x\to\:0+}(x^{2}\ln(x^{2}))
integral of (4x-x^2)^2	\int\:(4x-x^{2})^{2}dx
derivative of e^tcos(2t)	derivative\:e^{t}\cos(2t)
inverse oflaplace-1{(15)/(s^2+4s+13)}	inverselaplace\:-1\left\{\frac{15}{s^{2}+4s+13}\right\}
derivative of y=e^{x+1}+1	derivative\:y=e^{x+1}+1
x(dy)/(dx)+2y= 1/(x^3)	x\frac{dy}{dx}+2y=\frac{1}{x^{3}}
derivative of x^2+7x-5	derivative\:x^{2}+7x-5
integral of (3/(sqrt(x))-(xsqrt(x))/4)	\int\:(\frac{3}{\sqrt{x}}-\frac{x\sqrt{x}}{4})dx
z^'	z^{\prime\:}
derivative of y^2+x^2	\frac{d}{dx}(y^{2}+x^{2})
x^2((dy)/(dx))=y-xy	x^{2}(\frac{dy}{dx})=y-xy
area y=4-x^2,(1,2)	area\:y=4-x^{2},(1,2)
(dy)/(dx)= y/(y+x)	\frac{dy}{dx}=\frac{y}{y+x}
derivative of 2x^2y+4	\frac{d}{dx}(2x^{2}y+4)
derivative of (x^2-3x-4/(x-2))	\frac{d}{dx}(\frac{x^{2}-3x-4}{x-2})
limit as x approaches infinity of x+1/2	\lim\:_{x\to\:\infty\:}(x+\frac{1}{2})
(\partial)/(\partial x)(2xy+2y-x^2-2y^2)	\frac{\partial\:}{\partial\:x}(2xy+2y-x^{2}-2y^{2})
derivative of 1+x/(sqrt(1-x^2))	\frac{d}{dx}(1+\frac{x}{\sqrt{1-x^{2}}})
integral of (2sqrt(x))/(sqrt(x))	\int\:\frac{2\sqrt{x}}{\sqrt{x}}dx
integral of (sin(2x))/(17+cos^2(x))	\int\:\frac{\sin(2x)}{17+\cos^{2}(x)}dx
(\partial)/(\partial x)(4ycos(9x))	\frac{\partial\:}{\partial\:x}(4y\cos(9x))
area-x^2+3,2x+3	area\:-x^{2}+3,2x+3
integral of (2/x+3sin(x)-4ex)	\int\:(\frac{2}{x}+3\sin(x)-4ex)dx
derivative of 4x-8y^3	\frac{d}{dx}(4x-8y^{3})
y^{''}+y^'=x	y^{\prime\:\prime\:}+y^{\prime\:}=x
integral from 0 to 1 of (2x+1)e^{x^2+x}	\int\:_{0}^{1}(2x+1)e^{x^{2}+x}dx
(\partial)/(\partial x)(y^2arctan(x))	\frac{\partial\:}{\partial\:x}(y^{2}\arctan(x))
(\partial)/(\partial x)((x+y)/(y-x))	\frac{\partial\:}{\partial\:x}(\frac{x+y}{y-x})
limit as x approaches 0 of-x^2+1	\lim\:_{x\to\:0}(-x^{2}+1)
integral from 1 to 25 of 5xe^{2x}	\int\:_{1}^{25}5xe^{2x}dx
integral from 1 to 2 of ((x^2-1))/(x+1)	\int\:_{1}^{2}\frac{(x^{2}-1)}{x+1}dx
derivative of f(x)=(cx^2)/(x^2+b)	derivative\:f(x)=\frac{cx^{2}}{x^{2}+b}
(\partial)/(\partial x)(5x+y(x^2+y^2))	\frac{\partial\:}{\partial\:x}(5x+y(x^{2}+y^{2}))
integral of e^x-2cos(x)	\int\:e^{x}-2\cos(x)dx
tangent of y=ln(7-9x^2+8x^4),\at x=1	tangent\:y=\ln(7-9x^{2}+8x^{4}),\at\:x=1
tangent of y=x^2+3,(-3,12)	tangent\:y=x^{2}+3,(-3,12)
sum from n=1 to infinity of 1/((-3)^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{(-3)^{n}}
derivative of (2x^2+4x+8/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}+4x+8}{\sqrt{x}})
integral of x(e^{x^2})	\int\:x(e^{x^{2}})dx
derivative of x/6-6/x	\frac{d}{dx}(\frac{x}{6}-\frac{6}{x})
integral of sqrt(x/(x-1))	\int\:\sqrt{\frac{x}{x-1}}dx
derivative of csc^3(2x)	\frac{d}{dx}(\csc^{3}(2x))
derivative of (xy)^{1/2}	derivative\:(xy)^{\frac{1}{2}}
tangent of x^4-20x^2+64	tangent\:x^{4}-20x^{2}+64
integral of 1/(pln(p/x))	\int\:\frac{1}{p\ln(\frac{p}{x})}dp
derivative of x^5y	\frac{d}{dx}(x^{5}y)
integral of 6x^2-x^3	\int\:6x^{2}-x^{3}dx
integral of (cos(x))/(4+sin(x))	\int\:\frac{\cos(x)}{4+\sin(x)}dx
integral of (2-5x)/(x^6)	\int\:\frac{2-5x}{x^{6}}dx
(dy)/(dx)+(2xy)/(x^2+1)=x	\frac{dy}{dx}+\frac{2xy}{x^{2}+1}=x
tangent of 3/(x^2)	tangent\:\frac{3}{x^{2}}
integral of 1/(x^2sqrt(x^2+9))	\int\:\frac{1}{x^{2}\sqrt{x^{2}+9}}dx
limit as x approaches 3 of 7x+\|x-3\|	\lim\:_{x\to\:3}(7x+\left\|x-3\right\|)
(\partial)/(\partial x)(e^y+xe^{xy})	\frac{\partial\:}{\partial\:x}(e^{y}+xe^{xy})
derivative of x^3f(x)	derivative\:x^{3}f(x)
integral from 3 to 6 of 4	\int\:_{3}^{6}4dx
(\partial)/(\partial x)((x+2)^2-2(y-1)^2-5)	\frac{\partial\:}{\partial\:x}((x+2)^{2}-2(y-1)^{2}-5)
taylor sin(x)+cos(x)	taylor\:\sin(x)+\cos(x)
y^{''}+4y^'+3y=x	y^{\prime\:\prime\:}+4y^{\prime\:}+3y=x
tangent of f(x)=sqrt(x+5),\at x=11	tangent\:f(x)=\sqrt{x+5},\at\:x=11
tangent of sqrt(3x-5)	tangent\:\sqrt{3x-5}
integral of 1/(sqrt(x))e^{-sqrt(x)}	\int\:\frac{1}{\sqrt{x}}e^{-\sqrt{x}}dx
derivative of 4x^3e^{2x}	\frac{d}{dx}(4x^{3}e^{2x})
derivative of (x+1/x (x-1/x))	\frac{d}{dx}((x+\frac{1}{x})(x-\frac{1}{x}))
integral of e^{2x}+sin(-x)	\int\:e^{2x}+\sin(-x)dx
derivative of y=xsin(2/x)	derivative\:y=x\sin(\frac{2}{x})
derivative of sin^2(mx+ny(x))	\frac{d}{dx}(\sin^{2}(mx+ny(x)))
t^2y^{''}-2ty^'+2y=tln(t)	t^{2}y^{\prime\:\prime\:}-2ty^{\prime\:}+2y=t\ln(t)
tangent of x^2+xy+y^2=7,(2,1)	tangent\:x^{2}+xy+y^{2}=7,(2,1)
derivative of 4x^5-3x^m+2x^n+5x^2-x-6	\frac{d}{dx}(4x^{5}-3x^{m}+2x^{n}+5x^{2}-x-6)
(\partial)/(\partial x)(3y^2+12xy)	\frac{\partial\:}{\partial\:x}(3y^{2}+12xy)
y^'=3y^2e^x-2y	y^{\prime\:}=3y^{2}e^{x}-2y
limit as x approaches 0 of+(sin(x)ln(x))	\lim\:_{x\to\:0}(+(\sin(x)\ln(x)))
(dy)/(dx)=(x+2y)^2	\frac{dy}{dx}=(x+2y)^{2}
integral of 3\sqrt[4]{x^3}-8x^5+6e^x-2	\int\:3\sqrt[4]{x^{3}}-8x^{5}+6e^{x}-2dx
x^'=-x+sin(t)	x^{\prime\:}=-x+\sin(t)
(\partial)/(\partial x)((3x^5-7)/(4x))	\frac{\partial\:}{\partial\:x}(\frac{3x^{5}-7}{4x})
limit as x approaches 8 of 1/((x-8)^2)	\lim\:_{x\to\:8}(\frac{1}{(x-8)^{2}})
integral of ((tan^3(ln(x))))/(3x)	\int\:\frac{(\tan^{3}(\ln(x)))}{3x}dx
tangent of (4x+5)^5,\at x=-1	tangent\:(4x+5)^{5},\at\:x=-1
derivative of (e^x/(8x^2+1))	\frac{d}{dx}(\frac{e^{x}}{8x^{2}+1})
csc(y)dx+sec(x)dy=0	\csc(y)dx+\sec(x)dy=0
derivative of f(x)=e^{2x}arcsin(x)	derivative\:f(x)=e^{2x}\arcsin(x)
derivative of 10-x^2	\frac{d}{dx}(10-x^{2})
slope of y=x^3-9x	slope\:y=x^{3}-9x
integral of x^2sqrt(5+x)	\int\:x^{2}\sqrt{5+x}dx
(dy)/(dx)=-9y	\frac{dy}{dx}=-9y
limit as x approaches-3 of x(-3)	\lim\:_{x\to\:-3}(x(-3))
integral of 5e^{x^2}	\int\:5e^{x^{2}}dx
integral of 1/(x^2)+20x^{1/4}	\int\:\frac{1}{x^{2}}+20x^{\frac{1}{4}}dx

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