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Popular Calculus Problems

integral of (x^2+1)(4x-3)	\int\:(x^{2}+1)(4x-3)dx
integral of (4x^3)/(1-x^4)	\int\:\frac{4x^{3}}{1-x^{4}}dx
integral of x^5sqrt(6x^6+2)	\int\:x^{5}\sqrt{6x^{6}+2}dx
integral of (4x^2+3)^2	\int\:(4x^{2}+3)^{2}dx
area x^2-x,2x-2x^2	area\:x^{2}-x,2x-2x^{2}
limit as x approaches 4 of 1/(sqrt(x)+2)	\lim\:_{x\to\:4}(\frac{1}{\sqrt{x}+2})
derivative of e^x-6x^5	derivative\:e^{x}-6x^{5}
integral of (3x^2-4)^2x^3	\int\:(3x^{2}-4)^{2}x^{3}dx
(\partial)/(\partial y)(e^x)	\frac{\partial\:}{\partial\:y}(e^{x})
(\partial)/(\partial x)(5y-2x)	\frac{\partial\:}{\partial\:x}(5y-2x)
30(d^2y)/(dx^2)-10(dy)/(dx)=0	30\frac{d^{2}y}{dx^{2}}-10\frac{dy}{dx}=0
limit as x approaches 0 of (x+x^2)/(\|x\|)	\lim\:_{x\to\:0}(\frac{x+x^{2}}{\left\|x\right\|})
derivative of x(x^2-5)	\frac{d}{dx}(x(x^{2}-5))
integral from 0.2588 to 1 of e^{-ipi^2ws}	\int\:_{0.2588}^{1}e^{-iπ^{2}ws}dw
integral of x^3ln(1+x)	\int\:x^{3}\ln(1+x)dx
tangent of f(x)=(4x+1)^2,\at x=0	tangent\:f(x)=(4x+1)^{2},\at\:x=0
taylor (x+1)*ln(x)	taylor\:(x+1)\cdot\:\ln(x)
integral of 1/(e^x)cos(pi)x	\int\:\frac{1}{e^{x}}\cos(π)xdx
y^'=10xy	y^{\prime\:}=10xy
integral of 1/20 (x+1)^2(x-3)(x+4)	\int\:\frac{1}{20}(x+1)^{2}(x-3)(x+4)dx
y^{''}+4y^'-4y=0	y^{\prime\:\prime\:}+4y^{\prime\:}-4y=0
tangent of f(x)=(e^x)/x	tangent\:f(x)=\frac{e^{x}}{x}
derivative of 5cos^2(x)+5sin(x)	derivative\:5\cos^{2}(x)+5\sin(x)
derivative of (-6+sqrt(x)/(6+sqrt(x)))	\frac{d}{dx}(\frac{-6+\sqrt{x}}{6+\sqrt{x}})
derivative of sqrt(x)(x^4+1/(x^2))	\frac{d}{dx}(\sqrt{x}(x^{4}+\frac{1}{x^{2}}))
integral of (x^5ln(x))	\int\:(x^{5}\ln(x))dx
integral from 0 to 1 of 2/(sqrt(x)(1+x))	\int\:_{0}^{1}\frac{2}{\sqrt{x}(1+x)}dx
f(x)=arcsin(sqrt(x))	f(x)=\arcsin(\sqrt{x})
inverse oflaplace 2/(4s^2-8s)	inverselaplace\:\frac{2}{4s^{2}-8s}
integral from 2 to 4 of ((2x-3)x)/6	\int\:_{2}^{4}\frac{(2x-3)x}{6}dx
limit as x approaches-2 of-x^2+6x-1	\lim\:_{x\to\:-2}(-x^{2}+6x-1)
derivative of f(x)=2x+3/x	derivative\:f(x)=2x+\frac{3}{x}
limit as x approaches 4 of 5/(x+2)	\lim\:_{x\to\:4}(\frac{5}{x+2})
integral of ((x-1)/(x+1))^2	\int\:(\frac{x-1}{x+1})^{2}dx
slope of (0,2),(-1,-1)	slope\:(0,2),(-1,-1)
integral from-1 to 1 of (t^2-2)	\int\:_{-1}^{1}(t^{2}-2)dt
limit as x approaches infinity of-5pix	\lim\:_{x\to\:\infty\:}(-5πx)
tangent of y= 1/(x-8),(-1,-1/9)	tangent\:y=\frac{1}{x-8},(-1,-\frac{1}{9})
derivative of x^2-2x-3	\frac{d}{dx}(x^{2}-2x-3)
limit as x approaches 0 of (sin(mx))/x	\lim\:_{x\to\:0}(\frac{\sin(mx)}{x})
integral of x^3+2x^2-3x	\int\:x^{3}+2x^{2}-3xdx
y^'=3+t-y	y^{\prime\:}=3+t-y
derivative of 10e^{-x}	\frac{d}{dx}(10e^{-x})
(\partial)/(\partial x)(ln(4x^2))	\frac{\partial\:}{\partial\:x}(\ln(4x^{2}))
(d^2)/(dx^2)(e^xsin(x))	\frac{d^{2}}{dx^{2}}(e^{x}\sin(x))
integral of e^{t/(50)}	\int\:e^{\frac{t}{50}}dt
integral from 1 to 2 of ((x+1)^2)/x	\int\:_{1}^{2}\frac{(x+1)^{2}}{x}dx
derivative of x(ln(x)^2)	\frac{d}{dx}(x(\ln(x))^{2})
integral of (ln(x)-1)/((ln(x))^2)	\int\:\frac{\ln(x)-1}{(\ln(x))^{2}}dx
limit as h approaches 0 of ((x+h)^{-5}-x^{-5})/h	\lim\:_{h\to\:0}(\frac{(x+h)^{-5}-x^{-5}}{h})
integral of (sqrt(x))/(sqrt(x+1))	\int\:\frac{\sqrt{x}}{\sqrt{x+1}}dx
t^2y^2+e^{1/t}+(2yt^3+t^2y^3)y^'=0	t^{2}y^{2}+e^{\frac{1}{t}}+(2yt^{3}+t^{2}y^{3})y^{\prime\:}=0
y^{''}+8y^'+25y=0	y^{\prime\:\prime\:}+8y^{\prime\:}+25y=0
integral of (9sqrt(x^3)+7\sqrt[3]{x^2})	\int\:(9\sqrt{x^{3}}+7\sqrt[3]{x^{2}})dx
tangent of y=x^3-2x+1,(2,5)	tangent\:y=x^{3}-2x+1,(2,5)
integral from-2 to 1 of \|x\|	\int\:_{-2}^{1}\left\|x\right\|dx
(dy)/(dx)+ay=b	\frac{dy}{dx}+ay=b
integral of (x^3)/((7-x^4)^5)	\int\:\frac{x^{3}}{(7-x^{4})^{5}}dx
(\partial)/(\partial x)(e^{x(e^y)})	\frac{\partial\:}{\partial\:x}(e^{x(e^{y})})
derivative of 2(x-2)-cos(3x)*3	derivative\:2(x-2)-\cos(3x)\cdot\:3
integral of-e^{-t}	\int\:-e^{-t}dt
derivative of arcsec(2x)	\frac{d}{dx}(\arcsec(2x))
limit as x approaches 2 of x^2+3	\lim\:_{x\to\:2}(x^{2}+3)
integral from-2 to 2 of (2sqrt(4-x^2))^2	\int\:_{-2}^{2}(2\sqrt{4-x^{2}})^{2}dx
derivative of ((x^2-6x)/(x+1))	\frac{d}{dx}(\frac{(x^{2}-6x)}{x+1})
integral of xsqrt(x^2+9)	\int\:x\sqrt{x^{2}+9}dx
integral of (e^x+2)^2	\int\:(e^{x}+2)^{2}dx
(\partial)/(\partial x)(-5y^3sin(5x))	\frac{\partial\:}{\partial\:x}(-5y^{3}\sin(5x))
area y= 2/x ,y=8x,y= 1/8 x	area\:y=\frac{2}{x},y=8x,y=\frac{1}{8}x
integral from 2 to infinity of 1/(ln(x))	\int\:_{2}^{\infty\:}\frac{1}{\ln(x)}dx
limit as x approaches infinity of-1/2 e^{-x^2}	\lim\:_{x\to\:\infty\:}(-\frac{1}{2}e^{-x^{2}})
integral from 1 to 2 of cos((pix)/3)	\int\:_{1}^{2}\cos(\frac{πx}{3})dx
integral from 1 to 2 of 1/(sqrt(4-x^2))	\int\:_{1}^{2}\frac{1}{\sqrt{4-x^{2}}}dx
derivative of (5sqrt(x)+7x^2)	\frac{d}{dx}((5\sqrt{x}+7)x^{2})
derivative of e^{2x}cos(x)	\frac{d}{dx}(e^{2x}\cos(x))
integral of y/((x^2+y^2)^{3/2)}	\int\:\frac{y}{(x^{2}+y^{2})^{\frac{3}{2}}}dy
derivative of 5e^{8t+9}	derivative\:5e^{8t+9}
derivative of (2x^3+5)/x	derivative\:\frac{2x^{3}+5}{x}
derivative of y=sin^5(x)	derivative\:y=\sin^{5}(x)
integral of (x-2)/(x^2+3x)	\int\:\frac{x-2}{x^{2}+3x}dx
sum from n=0 to infinity of 2^{(3-2n)}	\sum\:_{n=0}^{\infty\:}2^{(3-2n)}
area x=1-y^2,x=y^2-1	area\:x=1-y^{2},x=y^{2}-1
derivative of (1-t^2)/((1+t^2)^2)	derivative\:\frac{1-t^{2}}{(1+t^{2})^{2}}
limit as x approaches 2 of (2x+5)^{x-3}	\lim\:_{x\to\:2}((2x+5)^{x-3})
tangent of (6x)/(x+5),\at x=-3	tangent\:\frac{6x}{x+5},\at\:x=-3
integral from-1 to 1 of 0	\int\:_{-1}^{1}0dx
sum from n=0 to infinity of 8/(5^n)	\sum\:_{n=0}^{\infty\:}\frac{8}{5^{n}}
derivative of (x^3+9)e^x	derivative\:(x^{3}+9)e^{x}
integral of (((x-2)^4))/(sqrt(4x-x^2))	\int\:\frac{((x-2)^{4})}{\sqrt{4x-x^{2}}}dx
derivative of ((-2x-3)^7)/((4x+2)^4)	derivative\:\frac{(-2x-3)^{7}}{(4x+2)^{4}}
derivative of (x^3+5/(x^2+1))	\frac{d}{dx}(\frac{x^{3}+5}{x^{2}+1})
limit as t approaches infinity of x	\lim\:_{t\to\:\infty\:}(x)
integral from 0 to 9 of pie^{-(2x)/9}	\int\:_{0}^{9}πe^{-\frac{2x}{9}}dx
integral of x^3sqrt(x^2+11)	\int\:x^{3}\sqrt{x^{2}+11}dx
(\partial)/(\partial x)(((xy))/(x-y))	\frac{\partial\:}{\partial\:x}(\frac{(xy)}{x-y})
integral from 1/2 to 5 of 14xln(2x)	\int\:_{\frac{1}{2}}^{5}14x\ln(2x)dx
(3x^2y+xy^2)dx+(x^3+x^2y)dy=0	(3x^{2}y+xy^{2})dx+(x^{3}+x^{2}y)dy=0
integral from 5 to 6 of x/(x^2+4x+20)	\int\:_{5}^{6}\frac{x}{x^{2}+4x+20}dx
y^{''}+4y^'+5y=e^x	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=e^{x}
derivative of-8e^{-8x}	\frac{d}{dx}(-8e^{-8x})

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