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Popular Calculus Problems

y^{''}-3y^'=-6x+4	y^{\prime\:\prime\:}-3y^{\prime\:}=-6x+4
area x^2-4x,x=0	area\:x^{2}-4x,x=0
derivative of (A+Bx+Cx^2/(x^2))	\frac{d}{dx}(\frac{A+Bx+Cx^{2}}{x^{2}})
derivative of sqrt(x)e^{xy}	\frac{d}{dx}(\sqrt{x}e^{xy})
(\partial)/(\partial x)(4e^x-2xe^y)	\frac{\partial\:}{\partial\:x}(4e^{x}-2xe^{y})
derivative of ln(u)	derivative\:\ln(u)
integral of (x^6)/(1+x^2)	\int\:\frac{x^{6}}{1+x^{2}}dx
derivative of (2x(3x^3))	\frac{d}{dx}((2x)(3x^{3}))
integral of x(x^2-8)^3	\int\:x(x^{2}-8)^{3}dx
integral of sin^5(x)cot(x)	\int\:\sin^{5}(x)\cot(x)dx
derivative of (ln(t))/t	derivative\:\frac{\ln(t)}{t}
integral of (sqrt(x^2-256))/x	\int\:\frac{\sqrt{x^{2}-256}}{x}dx
area x=-3,x=4,y=e^{2x},y=2e^{-x}	area\:x=-3,x=4,y=e^{2x},y=2e^{-x}
derivative of x^msqrt(a^2-x^2)	\frac{d}{dx}(x^{m}\sqrt{a^{2}-x^{2}})
(\partial)/(\partial x)(x^2+8xy+17y^2-2y+1)	\frac{\partial\:}{\partial\:x}(x^{2}+8xy+17y^{2}-2y+1)
(\partial)/(\partial x)(sin(2t))	\frac{\partial\:}{\partial\:x}(\sin(2t))
integral of (-8x^7y^{-5}+6x^6y^{-4})	\int\:(-8x^{7}y^{-5}+6x^{6}y^{-4})dy
integral from 1 to t of (31)/(x^3)	\int\:_{1}^{t}\frac{31}{x^{3}}dx
limit as x approaches 0 of (ln^2(x))/x	\lim\:_{x\to\:0}(\frac{\ln^{2}(x)}{x})
derivative of f(x)=ln^3(sqrt(3x-5))	derivative\:f(x)=\ln^{3}(\sqrt{3x-5})
integral of sec^2(t)+t(t^2+1)^3+t^2ln(t)	\int\:\sec^{2}(t)+t(t^{2}+1)^{3}+t^{2}\ln(t)dt
derivative of e^{sin(3x})	\frac{d}{dx}(e^{\sin(3x)})
y^'-2y=2-4x	y^{\prime\:}-2y=2-4x
(\partial)/(\partial x)((-18x)/((x-y)^4))	\frac{\partial\:}{\partial\:x}(\frac{-18x}{(x-y)^{4}})
derivative of y=4x^3-2x^2-2x	derivative\:y=4x^{3}-2x^{2}-2x
f(x)=(100)/(x^5)	f(x)=\frac{100}{x^{5}}
derivative of (x-1\|x-1\|)	\frac{d}{dx}((x-1)\left\|x-1\right\|)
integral from 1 to 4 of 6sqrt(t)ln(t)	\int\:_{1}^{4}6\sqrt{t}\ln(t)dt
integral of sec(2t)tan(2t)	\int\:\sec(2t)\tan(2t)dt
derivative of (8x-6)^2	derivative\:(8x-6)^{2}
derivative of y=2x-cot^2(x)	derivative\:y=2x-\cot^{2}(x)
integral of ((x^2+5)/((x+2)^2))	\int\:(\frac{x^{2}+5}{(x+2)^{2}})dx
integral of (x^3)/(x+2)	\int\:\frac{x^{3}}{x+2}dx
integral of y^2sin(y)	\int\:y^{2}\sin(y)dy
laplacetransform sin(2x+3)	laplacetransform\:\sin(2x+3)
limit as x approaches 0 of x^3cos(5/x)	\lim\:_{x\to\:0}(x^{3}\cos(\frac{5}{x}))
(\partial)/(\partial y)(x/(y+1))	\frac{\partial\:}{\partial\:y}(\frac{x}{y+1})
area y=3x^2,y=2-x,x=0	area\:y=3x^{2},y=2-x,x=0
integral of 4/(3x)	\int\:\frac{4}{3x}dx
derivative of y=ln(x^2+3)	derivative\:y=\ln(x^{2}+3)
sum from n=1 to infinity of (n!)/(100^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{100^{n}}
derivative of sin(5x+tan(3x))	\frac{d}{dx}(\sin(5x)+\tan(3x))
x^{''}+2x^'+10=e^{-t},x(0)=0,x^'(0)=0	x^{\prime\:\prime\:}+2x^{\prime\:}+10=e^{-t},x(0)=0,x^{\prime\:}(0)=0
f(x)=sin(\sqrt[3]{x})*cos(\sqrt[3]{x})	f(x)=\sin(\sqrt[3]{x})\cdot\:\cos(\sqrt[3]{x})
integral from 4 to infinity of 8x^{-3}	\int\:_{4}^{\infty\:}8x^{-3}dx
integral of 1/(sqrt(4x^2-9))	\int\:\frac{1}{\sqrt{4x^{2}-9}}dx
tangent of f(x)= 2/(x-2),(4,1)	tangent\:f(x)=\frac{2}{x-2},(4,1)
tangent of f(x)= 4/x	tangent\:f(x)=\frac{4}{x}
integral of (x^2+2x)*cos(x)	\int\:(x^{2}+2x)\cdot\:\cos(x)dx
integral of \sqrt[3]{x}(x-3)	\int\:\sqrt[3]{x}(x-3)dx
integral of x^2e^{-x^2}	\int\:x^{2}e^{-x^{2}}dx
integral of (4x^3-3x^2+2x-5)	\int\:(4x^{3}-3x^{2}+2x-5)dx
derivative of f(1/3 x^3)=2x^5	\frac{d}{dx}(f(\frac{1}{3}x^{3}))=2x^{5}
derivative of 2cos(x+(cos(x))^2)	\frac{d}{dx}(2\cos(x)+(\cos(x))^{2})
y^'=(y^4x^4+4x^4)/(y^3)	y^{\prime\:}=\frac{y^{4}x^{4}+4x^{4}}{y^{3}}
integral of (x+7)/(x^2(x+2))	\int\:\frac{x+7}{x^{2}(x+2)}dx
derivative of (cos(x2x^3)/(e^x))	\frac{d}{dx}(\frac{\cos(x)2x^{3}}{e^{x}})
integral of e^{2x}sin(-3x)	\int\:e^{2x}\sin(-3x)dx
limit as x approaches+1/5 of 2+\|5x-1\|	\lim\:_{x\to\:+\frac{1}{5}}(2+\left\|5x-1\right\|)
d/(dy)((y^3)/3+1/(4y))	\frac{d}{dy}(\frac{y^{3}}{3}+\frac{1}{4y})
integral from 0 to ln(20) of xe^x	\int\:_{0}^{\ln(20)}xe^{x}dx
integral of (12x^2+4x+2)/(x+x^2+2x^3)	\int\:\frac{12x^{2}+4x+2}{x+x^{2}+2x^{3}}dx
(\partial)/(\partial x)(5x+4y)	\frac{\partial\:}{\partial\:x}(5x+4y)
integral of (x^2+3x-2)^2	\int\:(x^{2}+3x-2)^{2}dx
derivative of g(x)=y=2x,x=1	derivative\:g(x)=y=2x,x=1
(\partial)/(\partial y)(ln(1+y^2))	\frac{\partial\:}{\partial\:y}(\ln(1+y^{2}))
integral of sin(t/2)	\int\:\sin(\frac{t}{2})dt
integral of x^9e^{x^{10-9}}	\int\:x^{9}e^{x^{10-9}}dx
integral of 1/50 x	\int\:\frac{1}{50}xdx
(x+y)dx-xdy=0	(x+y)dx-xdy=0
integral from 0 to 1 of x^7	\int\:_{0}^{1}x^{7}dx
limit as x approaches-5-of 2/(x+5)	\lim\:_{x\to\:-5-}(\frac{2}{x+5})
tangent of f(x)=x^2+2,(4,18)	tangent\:f(x)=x^{2}+2,(4,18)
limit as x approaches-9+of (x+10)/(x+9)	\lim\:_{x\to\:-9+}(\frac{x+10}{x+9})
limit as x approaches-2+of-3x+5	\lim\:_{x\to\:-2+}(-3x+5)
limit as x approaches 5+of (\|x-5\|)/(x-5)	\lim\:_{x\to\:5+}(\frac{\left\|x-5\right\|}{x-5})
integral of 1/(2+7x^2)	\int\:\frac{1}{2+7x^{2}}dx
derivative of (1/2 ^x)	\frac{d}{dx}((\frac{1}{2})^{x})
y^{''}-9y^'+3y=xe^x	y^{\prime\:\prime\:}-9y^{\prime\:}+3y=xe^{x}
integral of (x^3+x^2+2x-3)	\int\:(x^{3}+x^{2}+2x-3)dx
derivative of (ax^2+bx+ce^{-x/6})	\frac{d}{dx}((ax^{2}+bx+c)e^{-\frac{x}{6}})
derivative of y=7sin(4x)	derivative\:y=7\sin(4x)
(\partial)/(\partial y)(x^2y^5)	\frac{\partial\:}{\partial\:y}(x^{2}y^{5})
limit as x approaches 1+of-2	\lim\:_{x\to\:1+}(-2)
y^'+2y=x^2y^3	y^{\prime\:}+2y=x^{2}y^{3}
f(x)=x^9e^x	f(x)=x^{9}e^{x}
derivative of inx^2	\frac{d}{dx}(inx^{2})
integral from 0 to pi/4 of 49sin^2(x)	\int\:_{0}^{\frac{π}{4}}49\sin^{2}(x)dx
integral of sec^7(x)	\int\:\sec^{7}(x)dx
(dy)/(dx)=cot(x+y+3)-1	\frac{dy}{dx}=\cot(x+y+3)-1
integral of (e^{2x}-1)/(e^{2x)+1}	\int\:\frac{e^{2x}-1}{e^{2x}+1}dx
limit as x approaches 6+of (8+x)/(6-x)	\lim\:_{x\to\:6+}(\frac{8+x}{6-x})
integral of x^3e^{(x^2)}	\int\:x^{3}e^{(x^{2})}dx
integral of (8x+3)	\int\:(8x+3)dx
(\partial)/(\partial y)(e^{xy}ln(y))	\frac{\partial\:}{\partial\:y}(e^{xy}\ln(y))
derivative of 3/(1-6x)	derivative\:\frac{3}{1-6x}
y^'=e^{-3x}	y^{\prime\:}=e^{-3x}
limit as x approaches 5 of (\|x-5\|)/(x-5)	\lim\:_{x\to\:5}(\frac{\left\|x-5\right\|}{x-5})
integral from 1 to 5 of x^2ln(x)	\int\:_{1}^{5}x^{2}\ln(x)dx
(dy)/(dx)= 1/5 (8-y)	\frac{dy}{dx}=\frac{1}{5}(8-y)

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