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Popular Calculus Problems

integral of (13)/((x-2)(x^2+9))	\int\:\frac{13}{(x-2)(x^{2}+9)}dx
limit as x approaches 7+of 1/(x+7)	\lim\:_{x\to\:7+}(\frac{1}{x+7})
limit as x approaches 0 of (2sin(3x))/(5x)	\lim\:_{x\to\:0}(\frac{2\sin(3x)}{5x})
(\partial)/(\partial x)(9x^7cos(y^4))	\frac{\partial\:}{\partial\:x}(9x^{7}\cos(y^{4}))
y^{''}-3y^'-4y=e^{3t}	y^{\prime\:\prime\:}-3y^{\prime\:}-4y=e^{3t}
area y=(x^3)/2+(x^2)/2-2x,y=(x^2)/2	area\:y=\frac{x^{3}}{2}+\frac{x^{2}}{2}-2x,y=\frac{x^{2}}{2}
derivative of f(x)=cos^2(3x+1)	derivative\:f(x)=\cos^{2}(3x+1)
derivative of ln(4+x^2)	\frac{d}{dx}(\ln(4+x^{2}))
y^'-5y=9e^{8t}	y^{\prime\:}-5y=9e^{8t}
integral of 2/(2x+3)	\int\:\frac{2}{2x+3}dx
y^{''}+4y^'+5y=35e^{-4x},y(0)=-3,y^'(0)=1	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=35e^{-4x},y(0)=-3,y^{\prime\:}(0)=1
4x^'+x=5	4x^{\prime\:}+x=5
y^{1/2}y^'+y^{3/2}=1,y(0)=4	y^{\frac{1}{2}}y^{\prime\:}+y^{\frac{3}{2}}=1,y(0)=4
tangent of y=x^4+7e^x,(0,7)	tangent\:y=x^{4}+7e^{x},(0,7)
limit as x approaches 7+of 1/((x-7)^2)	\lim\:_{x\to\:7+}(\frac{1}{(x-7)^{2}})
integral of 1/(xsqrt(-1+x^2))	\int\:\frac{1}{x\sqrt{-1+x^{2}}}dx
derivative of f(x)=-8	derivative\:f(x)=-8
derivative of \sqrt[7]{t}	derivative\:\sqrt[7]{t}
derivative of \sqrt[3]{(2x+3)/(3x-5)}	derivative\:\sqrt[3]{\frac{2x+3}{3x-5}}
derivative of f(x)=sin(9ln(x))	derivative\:f(x)=\sin(9\ln(x))
y^{''}+4y=sin(x),y(0)=1,y^'(0)=4	y^{\prime\:\prime\:}+4y=\sin(x),y(0)=1,y^{\prime\:}(0)=4
integral of 4e^{x^2}	\int\:4e^{x^{2}}dx
integral from 0 to pi/4 of 2sec^2(x)	\int\:_{0}^{\frac{π}{4}}2\sec^{2}(x)dx
integral of (x+3)/(2x^3-8x)	\int\:\frac{x+3}{2x^{3}-8x}dx
tangent of y=2xtan(x),\at x=pi	tangent\:y=2x\tan(x),\at\:x=π
limit as x approaches 0 of (2x-1)/x	\lim\:_{x\to\:0}(\frac{2x-1}{x})
integral of (sin(2x))/(2cos^2(x))	\int\:\frac{\sin(2x)}{2\cos^{2}(x)}dx
area 1+x-x^2-x^3,1-x,[-2,1]	area\:1+x-x^{2}-x^{3},1-x,[-2,1]
(\partial)/(\partial y)(cos(yz))	\frac{\partial\:}{\partial\:y}(\cos(yz))
y^{''}-12y^'+38y=0	y^{\prime\:\prime\:}-12y^{\prime\:}+38y=0
integral of 1/2 cos^2(3θ)	\int\:\frac{1}{2}\cos^{2}(3θ)dθ
integral of r^2(r^3-4)^7	\int\:r^{2}(r^{3}-4)^{7}dr
derivative of xy+x	derivative\:xy+x
tangent of f(x)= 6/(x^2),(1,6)	tangent\:f(x)=\frac{6}{x^{2}},(1,6)
derivative of (f(x(3x))^2-4)	\frac{d}{dx}((f(x)(3x))^{2}-4)
integral from pi/3 to pi of sin(x)	\int\:_{\frac{π}{3}}^{π}\sin(x)dx
integral of (x^4-5x^2+2x)/(5x^2)	\int\:\frac{x^{4}-5x^{2}+2x}{5x^{2}}dx
derivative of 6+4/x+6/(x^2)	derivative\:6+\frac{4}{x}+\frac{6}{x^{2}}
integral of 4^x(4^x+1)^3	\int\:4^{x}(4^{x}+1)^{3}dx
slope ofintercept (-1/2 ,1),(-2, 1/2)	slopeintercept\:(-\frac{1}{2},1),(-2,\frac{1}{2})
integral of sqrt(4-y)	\int\:\sqrt{4-y}dy
derivative of (x-3xsqrt(x)/(sqrt(x)))	\frac{d}{dx}(\frac{x-3x\sqrt{x}}{\sqrt{x}})
derivative of sqrt((4+x^2)/(4-x))	derivative\:\sqrt{\frac{4+x^{2}}{4-x}}
tangent of f(x)=(12x-8)^{1/2},\at x=2	tangent\:f(x)=(12x-8)^{\frac{1}{2}},\at\:x=2
(dy)/(dx)=7xy^2	\frac{dy}{dx}=7xy^{2}
(\partial)/(\partial x)(3x^2y+2y)	\frac{\partial\:}{\partial\:x}(3x^{2}y+2y)
integral from 1 to 2 of xe^x	\int\:_{1}^{2}xe^{x}dx
derivative of f(x)=5^{sin(x)}	derivative\:f(x)=5^{\sin(x)}
integral from 1 to e of ln(11x)	\int\:_{1}^{e}\ln(11x)dx
integral of 5^{x^2}	\int\:5^{x^{2}}dx
integral of x/(sqrt(36-x^2))	\int\:\frac{x}{\sqrt{36-x^{2}}}dx
integral of (5x^3+5x)/(x-1)	\int\:\frac{5x^{3}+5x}{x-1}dx
y^'+y=e^t+11	y^{\prime\:}+y=e^{t}+11
derivative of 12x^3-36x^2	\frac{d}{dx}(12x^{3}-36x^{2})
(\partial)/(\partial x)(e^{-5x^2-4y^2})	\frac{\partial\:}{\partial\:x}(e^{-5x^{2}-4y^{2}})
derivative of f(x)=ln(x/(x^2+1))	derivative\:f(x)=\ln(\frac{x}{x^{2}+1})
integral of 5^tsin(5^t)	\int\:5^{t}\sin(5^{t})dt
sum from n=1 to infinity of (n/(n+10))^n	\sum\:_{n=1}^{\infty\:}(\frac{n}{n+10})^{n}
integral of cos^2(u)	\int\:\cos^{2}(u)du
integral from 0 to 25 of sqrt(x)	\int\:_{0}^{25}\sqrt{x}dx
xy^'=x^3+17x^3y	xy^{\prime\:}=x^{3}+17x^{3}y
integral of 4e^{9x}	\int\:4e^{9x}dx
tangent of f(x)=x^4-25x^2+144,\at x=1	tangent\:f(x)=x^{4}-25x^{2}+144,\at\:x=1
integral of 1 (y)	\int\:\frac{d}{1}(y)dx
derivative of tan^{1/x}(x)	\frac{d}{dx}(\tan^{\frac{1}{x}}(x))
integral of-3ln(x^2-1)	\int\:-3\ln(x^{2}-1)dx
derivative of ln(cos(x^2))	\frac{d}{dx}(\ln(\cos(x^{2})))
integral of sin^2((pix)/6)	\int\:\sin^{2}(\frac{πx}{6})dx
limit as x approaches 1+of x^{2/(1-x)}	\lim\:_{x\to\:1+}(x^{\frac{2}{1-x}})
derivative of 4+sqrt(7x)	derivative\:4+\sqrt{7x}
area y=2x,y=sqrt(x)	area\:y=2x,y=\sqrt{x}
derivative of sec(2x^3)	\frac{d}{dx}(\sec(2x^{3}))
derivative of (x-2/x+ln(x/2))	\frac{d}{dx}(\frac{x-2}{x}+\ln(\frac{x}{2}))
integral from-infinity to 5 of xe^x	\int\:_{-\infty\:}^{5}xe^{x}dx
1/((1+2y^2))y^'=csc(x)	\frac{1}{(1+2y^{2})}y^{\prime\:}=\csc(x)
limit as x approaches 0 of (x+e^{x/6})^{6/x}	\lim\:_{x\to\:0}((x+e^{\frac{x}{6}})^{\frac{6}{x}})
integral of (a+bx^3)^3	\int\:(a+bx^{3})^{3}dx
limit as x approaches 3 of-2x^3	\lim\:_{x\to\:3}(-2x^{3})
derivative of 1/(x+4)	derivative\:\frac{1}{x+4}
integral of (20)/((x-1)(x^2+9))	\int\:\frac{20}{(x-1)(x^{2}+9)}dx
derivative of 2/(x^2+1)	\frac{d}{dx}(\frac{2}{x^{2}+1})
derivative of (x^2+2sqrt(x))(1-e^x)	derivative\:(x^{2}+2\sqrt{x})(1-e^{x})
derivative of 8x+sqrt(x)	derivative\:8x+\sqrt{x}
derivative of (4x^5+7/(x^3))	\frac{d}{dx}(\frac{4x^{5}+7}{x^{3}})
y^{''}-2y^'+y=((-6e^t))/(t^2+1)	y^{\prime\:\prime\:}-2y^{\prime\:}+y=\frac{(-6e^{t})}{t^{2}+1}
derivative of f(x)=x^2arcsin(3x)	derivative\:f(x)=x^{2}\arcsin(3x)
f(x)=x^5e^x	f(x)=x^{5}e^{x}
(dr)/(dθ)=(sin(piθ))^4	\frac{dr}{dθ}=(\sin(πθ))^{4}
integral of 3e^{-x/2}	\int\:3e^{-\frac{x}{2}}dx
f(x)=3e^x	f(x)=3e^{x}
(\partial)/(\partial x)(3xy^2+16x^2y^3)	\frac{\partial\:}{\partial\:x}(3xy^{2}+16x^{2}y^{3})
integral of θtan(8)θ^2	\int\:θ\tan(8)θ^{2}dθ
(\partial)/(\partial x)(e^{xy}ln(9y))	\frac{\partial\:}{\partial\:x}(e^{xy}\ln(9y))
derivative of 5-2/x	\frac{d}{dx}(5-\frac{2}{x})
integral from 3 to infinity of (ln(x))/x	\int\:_{3}^{\infty\:}\frac{\ln(x)}{x}dx
tangent of f(x)=4e^xcos(x),(0,4)	tangent\:f(x)=4e^{x}\cos(x),(0,4)
derivative of (2x-3)e^{3x}	derivative\:(2x-3)e^{3x}
(dy)/(dx)+2y=e^{3x}y^2	\frac{dy}{dx}+2y=e^{3x}y^{2}
integral of x\sqrt[3]{x^2}-3	\int\:x\sqrt[3]{x^{2}}-3dx
integral of 1/(1+sqrt(1-x^2))	\int\:\frac{1}{1+\sqrt{1-x^{2}}}dx

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