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Popular Calculus Problems

derivative of xsinh(x-cosh(x))	\frac{d}{dx}(x\sinh(x)-\cosh(x))
integral of (3x)/(x^2+5)	\int\:\frac{3x}{x^{2}+5}dx
integral of csc^2(5x)	\int\:\csc^{2}(5x)dx
integral from 1 to 7 of (t^2-4t-12)	\int\:_{1}^{7}(t^{2}-4t-12)dt
limit as x approaches 4-of 1+sqrt(4-x)	\lim\:_{x\to\:4-}(1+\sqrt{4-x})
derivative of y=(x^5+2)^2(x^4+4)^4	derivative\:y=(x^{5}+2)^{2}(x^{4}+4)^{4}
sum from n=1 to infinity of (-1)^nsin(2/n)	\sum\:_{n=1}^{\infty\:}(-1)^{n}\sin(\frac{2}{n})
derivative of (4x+x^2)/((2+x)^2)	derivative\:\frac{4x+x^{2}}{(2+x)^{2}}
integral of \sqrt[7]{e^x}	\int\:\sqrt[7]{e^{x}}dx
derivative of (x^2+y^2^3)	\frac{d}{dx}((x^{2}+y^{2})^{3})
extreme f(x)=4xy	extreme\:f(x)=4xy
y^{''}+4y=8x^2,y(0)=-3,y^'(0)=0	y^{\prime\:\prime\:}+4y=8x^{2},y(0)=-3,y^{\prime\:}(0)=0
derivative of (e^{2x}/(x^3))	\frac{d}{dx}(\frac{e^{2x}}{x^{3}})
integral of 1/(x(ln(x^2))^4)	\int\:\frac{1}{x(\ln(x^{2}))^{4}}dx
derivative of (x^2+3/(2x))	\frac{d}{dx}(\frac{x^{2}+3}{2x})
integral of (7-98x)/(sqrt(4-49x^2))	\int\:\frac{7-98x}{\sqrt{4-49x^{2}}}dx
xln(x)(dy)/(dx)+y=xe^x	x\ln(x)\frac{dy}{dx}+y=xe^{x}
integral of \|x-1\|	\int\:\left\|x-1\right\|dx
derivative of f(x)=e^6	derivative\:f(x)=e^{6}
(\partial)/(\partial x)(x^2+w^2)	\frac{\partial\:}{\partial\:x}(x^{2}+w^{2})
integral of ((2x+2))/((x^2+1)(x-1)^3)	\int\:\frac{(2x+2)}{(x^{2}+1)(x-1)^{3}}dx
derivative of y=(arctan(2x))^2	derivative\:y=(\arctan(2x))^{2}
derivative of arctan(sqrt(x^3))	\frac{d}{dx}(\arctan(\sqrt{x^{3}}))
derivative of arcsin(5x^2)	\frac{d}{dx}(\arcsin(5x^{2}))
y^'=(2y+1)cot(x)	y^{\prime\:}=(2y+1)\cot(x)
derivative of (3x^2/(x^2+1))	\frac{d}{dx}(\frac{3x^{2}}{x^{2}+1})
derivative of y=(4x^2+6x)/(3x^3+2)	derivative\:y=\frac{4x^{2}+6x}{3x^{3}+2}
y^'=2y(1-y/(6200))	y^{\prime\:}=2y(1-\frac{y}{6200})
integral of (x^7e^{x^8})	\int\:(x^{7}e^{x^{8}})dx
integral of sqrt((a+x)/(a-x))	\int\:\sqrt{\frac{a+x}{a-x}}dx
sum from n=1 to infinity of n/((n^2+1))	\sum\:_{n=1}^{\infty\:}\frac{n}{(n^{2}+1)}
integral of (4x^2-21x)/((x-3)^2(2x+3))	\int\:\frac{4x^{2}-21x}{(x-3)^{2}(2x+3)}dx
integral of (ln(x)-1)/(x^2)	\int\:\frac{\ln(x)-1}{x^{2}}dx
derivative of tan(x+pi/4)	\frac{d}{dx}(\tan(x+\frac{π}{4}))
simplify cos(arctan(x))	simplify\:\cos(\arctan(x))
derivative of sec^2(5x)	derivative\:\sec^{2}(5x)
derivative of sqrt(5)	derivative\:\sqrt{5}
derivative of ln((x^2)/(3x+1))	derivative\:\ln(\frac{x^{2}}{3x+1})
integral from 1 to 1 of x^2	\int\:_{1}^{1}x^{2}dx
integral of-e^{-x}cos(3x)	\int\:-e^{-x}\cos(3x)dx
limit as x approaches infinity of x^{6x}	\lim\:_{x\to\:\infty\:}(x^{6x})
derivative of ln(sqrt(x+9))	derivative\:\ln(\sqrt{x+9})
derivative of (x^9/9-(x^7)/7)	\frac{d}{dx}(\frac{x^{9}}{9}-\frac{x^{7}}{7})
limit as x approaches 1 of (e^{x^2-1})/(x^2-3x+2)	\lim\:_{x\to\:1}(\frac{e^{x^{2}-1}}{x^{2}-3x+2})
(dy)/(dx)=((y-1))/(x^2)	\frac{dy}{dx}=\frac{(y-1)}{x^{2}}
derivative of 6cos(2x)	derivative\:6\cos(2x)
integral of (100)/(sqrt(36+25x^2))	\int\:\frac{100}{\sqrt{36+25x^{2}}}dx
sum from n=1 to infinity of ne^{-n}	\sum\:_{n=1}^{\infty\:}ne^{-n}
2y^'=y^3*cos(x)	2y^{\prime\:}=y^{3}\cdot\:\cos(x)
xy^'+2y=-4cos(x)	xy^{\prime\:}+2y=-4\cos(x)
integral of arcsin((2x)/5)	\int\:\arcsin(\frac{2x}{5})dx
integral of 1/(1-x^4)	\int\:\frac{1}{1-x^{4}}dx
integral of 6/((1-x^2)^{3/2)}	\int\:\frac{6}{(1-x^{2})^{\frac{3}{2}}}dx
derivative of y=x^{-3}+5x^{-2}	derivative\:y=x^{-3}+5x^{-2}
y^'=(x-y)/(x+y),y(0)=1	y^{\prime\:}=\frac{x-y}{x+y},y(0)=1
slope of x^2+3x+5	slope\:x^{2}+3x+5
taylor 1/(1-\frac{1){1-x}}	taylor\:\frac{1}{1-\frac{1}{1-x}}
derivative of sqrt(3)x+sqrt(7x)	\frac{d}{dx}(\sqrt{3}x+\sqrt{7x})
tangent of y=2x^3+3x^2-12x+3	tangent\:y=2x^{3}+3x^{2}-12x+3
derivative of (2-sqrt(x)^4)	\frac{d}{dx}((2-\sqrt{x})^{4})
y^'+2y=e^{-x}	y^{\prime\:}+2y=e^{-x}
xy^'=2x+3y	xy^{\prime\:}=2x+3y
integral of (x^5-3125)/(x-5)	\int\:\frac{x^{5}-3125}{x-5}dx
tangent of f(x)=3x^2+12x-36	tangent\:f(x)=3x^{2}+12x-36
integral of-(10)/(sqrt(x^2+16))	\int\:-\frac{10}{\sqrt{x^{2}+16}}dx
-y^{''}+36y=0	-y^{\prime\:\prime\:}+36y=0
derivative of x^{7/2}	\frac{d}{dx}(x^{\frac{7}{2}})
derivative of 6y	derivative\:6y
integral of (1/(x^2))	\int\:(\frac{1}{x^{2}})dx
integral of (cos^2(2x))/4	\int\:\frac{\cos^{2}(2x)}{4}dx
limit as x approaches infinity of 5/x-2	\lim\:_{x\to\:\infty\:}(\frac{5}{x}-2)
maclaurin f(x)=x^4sin(4x)	maclaurin\:f(x)=x^{4}\sin(4x)
y^{''}+9y=cos(3x)+sin(3x)	y^{\prime\:\prime\:}+9y=\cos(3x)+\sin(3x)
sum from n=3 to infinity of (3^n)/(10^n)	\sum\:_{n=3}^{\infty\:}\frac{3^{n}}{10^{n}}
(\partial)/(\partial x)(1/(ln(2/x)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\ln(\frac{2}{x})})
y^{''}+6y^'+8y=e^{2x}	y^{\prime\:\prime\:}+6y^{\prime\:}+8y=e^{2x}
integral of e^{2-5x}	\int\:e^{2-5x}dx
integral of {(3-x)/(x^2+1)+xln(x^2)}	\int\:\left\{\frac{3-x}{x^{2}+1}+x\ln(x^{2})\right\}dx
integral of (x^2+4)/(x+1)	\int\:\frac{x^{2}+4}{x+1}dx
derivative of g(x)=x^2(1-7x)	derivative\:g(x)=x^{2}(1-7x)
derivative of ((x+7/(x-7))^5)	\frac{d}{dx}((\frac{x+7}{x-7})^{5})
derivative of sqrt((x+3))	derivative\:\sqrt{(x+3)}
limit as x approaches 0+of (-1)/(14x)	\lim\:_{x\to\:0+}(\frac{-1}{14x})
integral of (sec(x/(24)))^2tan(x/(24))	\int\:(\sec(\frac{x}{24}))^{2}\tan(\frac{x}{24})dx
limit as h approaches 0 of (sinh(x))/h	\lim\:_{h\to\:0}(\frac{\sinh(x)}{h})
integral of 2cos(ln(x))	\int\:2\cos(\ln(x))dx
integral of sin(2x^2)	\int\:\sin(2x^{2})dx
y^'+4x^3y=x^3	y^{\prime\:}+4x^{3}y=x^{3}
integral of (1-x)sqrt(x)	\int\:(1-x)\sqrt{x}dx
limit as x approaches infinity of 0.6^x	\lim\:_{x\to\:\infty\:}(0.6^{x})
derivative of (x+(x+sin^2(x)^7)^3)	\frac{d}{dx}((x+(x+\sin^{2}(x))^{7})^{3})
integral of t^2e^{-t^3}	\int\:t^{2}e^{-t^{3}}dt
laplacetransform x^4	laplacetransform\:x^{4}
integral of sin((npix)/L)	\int\:\sin(\frac{nπx}{L})dx
integral of x^2arctan(5x)	\int\:x^{2}\arctan(5x)dx
integral of 4^{-2x}	\int\:4^{-2x}dx
derivative of (4x+1)^2	derivative\:(4x+1)^{2}
tangent of f(x)=(x^3-25x)^{14},(5,0)	tangent\:f(x)=(x^{3}-25x)^{14},(5,0)
limit as x approaches 2 of 12x^2	\lim\:_{x\to\:2}(12x^{2})
integral of (sech(1/x)tanh(1/x))/(x^2)	\int\:\frac{\sech(\frac{1}{x})\tanh(\frac{1}{x})}{x^{2}}dx

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