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Popular Calculus Problems

derivative of (x^3/(x^2+1))	\frac{d}{dx}(\frac{x^{3}}{x^{2}+1})
limit as x approaches 0 of (e^{-5x}-1)/x	\lim\:_{x\to\:0}(\frac{e^{-5x}-1}{x})
derivative of cos(5x^2-x)	\frac{d}{dx}(\cos(5x^{2}-x))
tangent of f(x)=2x^2+3x,\at x=-2	tangent\:f(x)=2x^{2}+3x,\at\:x=-2
derivative of 2/(x-2)	\frac{d}{dx}(\frac{2}{x-2})
derivative of 5e^{-x}+e^{4x}	\frac{d}{dx}(5e^{-x}+e^{4x})
x^3y^{'''}-x^2y^{''}+2xy^'-2y=x	x^{3}y^{\prime\:\prime\:\prime\:}-x^{2}y^{\prime\:\prime\:}+2xy^{\prime\:}-2y=x
integral from 0 to 1 of pi(x^2-x^6)	\int\:_{0}^{1}π(x^{2}-x^{6})dx
limit as t approaches 0 of (tan^2(3t))/(2t)	\lim\:_{t\to\:0}(\frac{\tan^{2}(3t)}{2t})
integral of e^{x/7}	\int\:e^{\frac{x}{7}}dx
integral of cos(2nt)	\int\:\cos(2nt)dt
integral from 1 to 7 of sqrt(t)ln(t)	\int\:_{1}^{7}\sqrt{t}\ln(t)dt
inverse oflaplace 3/(s(s^2+s+5))	inverselaplace\:\frac{3}{s(s^{2}+s+5)}
derivative of e^tsin(2t)	derivative\:e^{t}\sin(2t)
integral from 1 to sqrt(2 of)x2^{(x^2)}	\int\:_{1}^{\sqrt{2}}x2^{(x^{2})}dx
integral of ((x))/(sqrt(1-x^2))	\int\:\frac{(x)}{\sqrt{1-x^{2}}}dx
integral from 0 to infinity of x^{-3}	\int\:_{0}^{\infty\:}x^{-3}dx
(d^2y)/(dt^2)+3(dy)/(dt)-40y=1-4t	\frac{d^{2}y}{dt^{2}}+3\frac{dy}{dt}-40y=1-4t
integral of-1/2 cos(2x)	\int\:-\frac{1}{2}\cos(2x)dx
derivative of (2x+3)^2	derivative\:(2x+3)^{2}
derivative of-x^2y^2	\frac{d}{dx}(-x^{2}y^{2})
limit as x approaches 1-of 3x-2	\lim\:_{x\to\:1-}(3x-2)
integral of (x^2)/2 1/x	\int\:\frac{x^{2}}{2}\frac{1}{x}dx
xe^y(dy)/(dx)+e^y=e^x	xe^{y}\frac{dy}{dx}+e^{y}=e^{x}
derivative of e^{-x/2}sin((sqrt(3)/2 x))	\frac{d}{dx}(e^{-\frac{x}{2}}\sin(\frac{\sqrt{3}}{2}x))
derivative of 0.5x^34^x	derivative\:0.5x^{3}4^{x}
integral from 0 to 1/13 of xln(13x)	\int\:_{0}^{\frac{1}{13}}x\ln(13x)dx
y^{''}-12y^'+45y=0	y^{\prime\:\prime\:}-12y^{\prime\:}+45y=0
derivative of (x-sin(x)(x+cos(x)))	\frac{d}{dx}((x-\sin(x))(x+\cos(x)))
2x(dy)/(dx)+y^3e^{-2x}=2xy	2x\frac{dy}{dx}+y^{3}e^{-2x}=2xy
simplify cos(xy)	simplify\:\cos(xy)
(\partial)/(\partial x)(-10xe^{-5x^2-2y^2})	\frac{\partial\:}{\partial\:x}(-10xe^{-5x^{2}-2y^{2}})
integral of sqrt(6x+2)	\int\:\sqrt{6x+2}dx
derivative of f(x)=(3-2x-x^2)/(x^2-1)	derivative\:f(x)=\frac{3-2x-x^{2}}{x^{2}-1}
(dy)/(dx)=x(1+y)	\frac{dy}{dx}=x(1+y)
integral of 3/(x^2)+4sqrt(x)	\int\:\frac{3}{x^{2}}+4\sqrt{x}dx
limit as x approaches 0 of-e^{1/x}	\lim\:_{x\to\:0}(-e^{\frac{1}{x}})
factor 12-8x+x^2	factor\:12-8x+x^{2}
area y= 1/(sqrt(1-8x)),-10<= x<= 0	area\:y=\frac{1}{\sqrt{1-8x}},-10\le\:x\le\:0
derivative of sqrt(1+2x)-sqrt(1-4x)	\frac{d}{dx}(\sqrt{1+2x}-\sqrt{1-4x})
integral of 4/((x+1))	\int\:\frac{4}{(x+1)}dx
derivative of ln(e^{sin(x}*x^{cos(x)}))	\frac{d}{dx}(\ln(e^{\sin(x)}\cdot\:x^{\cos(x)}))
limit as x approaches-1 of x^3+3x^2-2x-3	\lim\:_{x\to\:-1}(x^{3}+3x^{2}-2x-3)
ty^'+4y=t^3,y(2)=4	ty^{\prime\:}+4y=t^{3},y(2)=4
derivative of w/(sqrt(1-4x^2))	\frac{d}{dx}(\frac{w}{\sqrt{1-4x^{2}}})
integral of 5x^{3/2}	\int\:5x^{\frac{3}{2}}dx
d/(dt)(1.1t+6.3t^3)	\frac{d}{dt}(1.1t+6.3t^{3})
integral of ((16x^2))/((sqrt(x^2+9))^5)	\int\:\frac{(16x^{2})}{(\sqrt{x^{2}+9})^{5}}dx
derivative of 2sinh(2x)	\frac{d}{dx}(2\sinh(2x))
derivative of y=sqrt(x/(x+9))	derivative\:y=\sqrt{\frac{x}{x+9}}
integral of 3x^2+3x^2ln(y)	\int\:3x^{2}+3x^{2}\ln(y)dx
integral of cot^2(5x)csc(5x)	\int\:\cot^{2}(5x)\csc(5x)dx
derivative of e^{-2t}cos(x)	\frac{d}{dx}(e^{-2t}\cos(x))
limit as x approaches 0 of (3\|x\|)/(x^2)	\lim\:_{x\to\:0}(\frac{3\left\|x\right\|}{x^{2}})
integral of ((65x+7))/((8x+1)(x-1))	\int\:\frac{(65x+7)}{(8x+1)(x-1)}dx
derivative of (e^{x^2}/(2x))	\frac{d}{dx}(\frac{e^{x^{2}}}{2x})
derivative of e^{-x^2-y^2}	\frac{d}{dx}(e^{-x^{2}-y^{2}})
integral of arccsc(x)	\int\:\arccsc(x)dx
(\partial)/(\partial x)(7xy^4+2)	\frac{\partial\:}{\partial\:x}(7xy^{4}+2)
sum from n=1 to infinity of (-10/11)^n	\sum\:_{n=1}^{\infty\:}(-\frac{10}{11})^{n}
integral of (50x)/(sec(5x^2+5))	\int\:\frac{50x}{\sec(5x^{2}+5)}dx
y^'=xy^3-xy	y^{\prime\:}=xy^{3}-xy
integral of 1/(tsqrt(t))	\int\:\frac{1}{t\sqrt{t}}dt
derivative of e^{-2ix}	\frac{d}{dx}(e^{-2ix})
derivative of ln(5x^4)	derivative\:\ln(5x^{4})
(\partial)/(\partial x)((e^{2y}-ycos(xy))dx)	\frac{\partial\:}{\partial\:x}((e^{2y}-y\cos(xy))dx)
integral of e^xsqrt(1+e^{2x)}	\int\:e^{x}\sqrt{1+e^{2x}}dx
derivative of y=x^{4^x}	derivative\:y=x^{4^{x}}
derivative of A(e^x+e^xx)	\frac{d}{dx}(A(e^{x}+e^{x}x))
9y^{''}+6y^'+y=0,y(-3)=-2,y^'(1)=-1	9y^{\prime\:\prime\:}+6y^{\prime\:}+y=0,y(-3)=-2,y^{\prime\:}(1)=-1
y^'=1+x^2+y^2+x^2y^2	y^{\prime\:}=1+x^{2}+y^{2}+x^{2}y^{2}
integral from 0 to 1 of y/(e^{2y)}	\int\:_{0}^{1}\frac{y}{e^{2y}}dy
(\partial)/(\partial y)(xy^3z^2)	\frac{\partial\:}{\partial\:y}(xy^{3}z^{2})
(\partial)/(\partial x)(x*Y(x))	\frac{\partial\:}{\partial\:x}(x\cdot\:Y(x))
area 5-x^2,sin(x),-2.385,2.025	area\:5-x^{2},\sin(x),-2.385,2.025
derivative of (4-x^2)^5	derivative\:(4-x^{2})^{5}
integral of (e^x+1/(3x))	\int\:(e^{x}+\frac{1}{3x})dx
derivative of (2/5 x)^9	derivative\:(\frac{2}{5}x)^{9}
integral from 0 to pi/4 of 2sec(t)	\int\:_{0}^{\frac{π}{4}}2\sec(t)dt
sum from n=1 to infinity of (-1)^n9^nx^n	\sum\:_{n=1}^{\infty\:}(-1)^{n}9^{n}x^{n}
derivative of sqrt(1+x)-1	\frac{d}{dx}(\sqrt{1+x}-1)
derivative of 3csc(x+7cos(x))	\frac{d}{dx}(3\csc(x)+7\cos(x))
derivative of (x+1/(x+1))	\frac{d}{dx}(\frac{x+1}{x+1})
integral of 64	\int\:64dx
sum from n=1 to infinity of 2(0.5)^{n-1}	\sum\:_{n=1}^{\infty\:}2(0.5)^{n-1}
tangent of 5x^2+5x+2	tangent\:5x^{2}+5x+2
limit as x approaches 3 of (4x^2-36)/(2x-6)	\lim\:_{x\to\:3}(\frac{4x^{2}-36}{2x-6})
integral from 1/2 to 1 of x^{-3}-11	\int\:_{\frac{1}{2}}^{1}x^{-3}-11dx
derivative of cos(x-5tan(x))	\frac{d}{dx}(\cos(x)-5\tan(x))
integral of (2x+3)/(sqrt(1+x^2))	\int\:\frac{2x+3}{\sqrt{1+x^{2}}}dx
integral of e^{6x}2^{9x}	\int\:e^{6x}2^{9x}dx
d/(dt)((cos(t))^2)	\frac{d}{dt}((\cos(t))^{2})
(\partial)/(\partial y)(xye^{-4y})	\frac{\partial\:}{\partial\:y}(xye^{-4y})
integral of 1/(xsqrt(7-x^2))	\int\:\frac{1}{x\sqrt{7-x^{2}}}dx
integral of 4x-2	\int\:4x-2dx
derivative of y=2Cx+C(sin(x)+xcos(x))	derivative\:y=2Cx+C(\sin(x)+x\cos(x))
sum from n=1 to infinity of (7/3)^n	\sum\:_{n=1}^{\infty\:}(\frac{7}{3})^{n}
derivative of f(x)=ln(11x)	derivative\:f(x)=\ln(11x)
(\partial)/(\partial x)(x^2(1+y^2))	\frac{\partial\:}{\partial\:x}(x^{2}(1+y^{2}))
integral from 0 to pi of 17sin^2(2x)	\int\:_{0}^{π}17\sin^{2}(2x)dx

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