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Popular Calculus Problems

integral from 4 to 7 of 1/(x-3)	\int\:_{4}^{7}\frac{1}{x-3}dx
integral of-4/3 x^3sqrt(2x-1)	\int\:-\frac{4}{3}x^{3}\sqrt{2x-1}dx
derivative of ln(x^2+1)	derivative\:\ln(x^{2}+1)
integral of 2xsin(x)e^x	\int\:2x\sin(x)e^{x}dx
derivative of ln(\sqrt[3]{x^3+8})	\frac{d}{dx}(\ln(\sqrt[3]{x^{3}+8}))
inverse oflaplace (e^{-4s})/(2s-1)	inverselaplace\:\frac{e^{-4s}}{2s-1}
derivative of x^2sin(x)	derivative\:x^{2}\sin(x)
limit as x approaches 1/5+of x/(10x-2)	\lim\:_{x\to\:\frac{1}{5}+}(\frac{x}{10x-2})
integral of (2x)/(sqrt(3x+1))	\int\:\frac{2x}{\sqrt{3x+1}}dx
integral of x(cos^3(x^2)-sin^3(x^2))	\int\:x(\cos^{3}(x^{2})-\sin^{3}(x^{2}))dx
derivative of x^3-9x^2+27x	\frac{d}{dx}(x^{3}-9x^{2}+27x)
integral of 1/(xsqrt(16x^2-5))	\int\:\frac{1}{x\sqrt{16x^{2}-5}}dx
integral of (a^2-x^2)^{(3/2)}	\int\:(a^{2}-x^{2})^{(\frac{3}{2})}dx
derivative of f(x)=12-120x	derivative\:f(x)=12-120x
integral of (e^x-26^x)	\int\:(e^{x}-26^{x})dx
derivative of 3sqrt(25-x^2)	derivative\:3\sqrt{25-x^{2}}
derivative of 9x^{7/2}	\frac{d}{dx}(9x^{\frac{7}{2}})
derivative of f(x)=(x^3+2x^2+x+2)/(x+2)	derivative\:f(x)=\frac{x^{3}+2x^{2}+x+2}{x+2}
integral of e^{-6x}tan(e^{-6x})	\int\:e^{-6x}\tan(e^{-6x})dx
y^'-((2x)/(1+x^2))y=0	y^{\prime\:}-(\frac{2x}{1+x^{2}})y=0
(\partial)/(\partial x)(10^x)	\frac{\partial\:}{\partial\:x}(10^{x})
limit as x approaches-3 of-f(x)	\lim\:_{x\to\:-3}(-f(x))
integral of (sin(x))/(cos(x)+(cos(x))^2)	\int\:\frac{\sin(x)}{\cos(x)+(\cos(x))^{2}}dx
integral from-1 to 1 of 5	\int\:_{-1}^{1}5dx
integral of sin^2(x/2)cos(x/3)	\int\:\sin^{2}(\frac{x}{2})\cos(\frac{x}{3})dx
integral of sin(x)(cos(x))^2	\int\:\sin(x)(\cos(x))^{2}dx
derivative of sqrt(sin(x-1x^3))	\frac{d}{dx}(\sqrt{\sin(x-1)x^{3}})
(\partial)/(\partial z)((xy)/(x^2+y^2))	\frac{\partial\:}{\partial\:z}(\frac{xy}{x^{2}+y^{2}})
derivative of 3/(x-6)	derivative\:\frac{3}{x-6}
y^{''}+2y^'+5y=0,y(0)=4,y^'(0)=-3	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=0,y(0)=4,y^{\prime\:}(0)=-3
integral of (4x)/(4x^2-12x+13)	\int\:\frac{4x}{4x^{2}-12x+13}dx
integral of x/(x^2+81)	\int\:\frac{x}{x^{2}+81}dx
(\partial)/(\partial z)(5zy+2)	\frac{\partial\:}{\partial\:z}(5zy+2)
integral from-33 to 0 of 1/(sqrt(16-x))	\int\:_{-33}^{0}\frac{1}{\sqrt{16-x}}dx
(\partial)/(\partial x)(1+3x^2y^2)	\frac{\partial\:}{\partial\:x}(1+3x^{2}y^{2})
(\partial)/(\partial x)(x^2y^3e^{xy})	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}e^{xy})
limit as x approaches infinity of (9x-x^2-7x^4)/(x^3+12x)	\lim\:_{x\to\:\infty\:}(\frac{9x-x^{2}-7x^{4}}{x^{3}+12x})
integral of ((x^6e^x))/x	\int\:\frac{(x^{6}e^{x})}{x}dx
integral of (1-x)x^3(x-2)^2	\int\:(1-x)x^{3}(x-2)^{2}dx
xy^'-2y=2x^2-2x-2	xy^{\prime\:}-2y=2x^{2}-2x-2
derivative of 5x^{0.5}	\frac{d}{dx}(5x^{0.5})
derivative of 6sqrt(x)+9	derivative\:6\sqrt{x}+9
integral of (e^x-1)/(e^x+1)	\int\:\frac{e^{x}-1}{e^{x}+1}dx
limit as x approaches 1+of x^2+1	\lim\:_{x\to\:1+}(x^{2}+1)
integral of x/(x^3-1)	\int\:\frac{x}{x^{3}-1}dx
derivative of \sqrt[3]{pix}	\frac{d}{dx}(\sqrt[3]{πx})
(\partial)/(\partial x)((2x^2y)/(2+x^2y^2))	\frac{\partial\:}{\partial\:x}(\frac{2x^{2}y}{2+x^{2}y^{2}})
simplify y/(y-x)	simplify\:\frac{y}{y-x}
derivative of ln(x-1+cos(x-1))	\frac{d}{dx}(\ln(x-1)+\cos(x-1))
integral from-1 to 1 of 1-x^2	\int\:_{-1}^{1}1-x^{2}dx
integral of cos(4x+2)	\int\:\cos(4x+2)dx
(\partial)/(\partial x)(10r^2sin(2x))	\frac{\partial\:}{\partial\:x}(10r^{2}\sin(2x))
integral of (2x^2-6x)e^{2x}	\int\:(2x^{2}-6x)e^{2x}dx
(\partial)/(\partial y)((x+y)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{x+y}{x^{2}+y^{2}})
derivative of (x^4/4-(x^3)/3-3x^2+4)	\frac{d}{dx}(\frac{x^{4}}{4}-\frac{x^{3}}{3}-3x^{2}+4)
integral of (4-3x)^7	\int\:(4-3x)^{7}dx
laplacetransform cos(2(t-pi/2))	laplacetransform\:\cos(2(t-\frac{π}{2}))
integral of-6sin(x)	\int\:-6\sin(x)dx
(dy)/(dx)-4/x y=y^5 1/(x^8)	\frac{dy}{dx}-\frac{4}{x}y=y^{5}\frac{1}{x^{8}}
integral of 3x(3-x^{-8})	\int\:3x(3-x^{-8})dx
derivative of 6cos^4(3x+2)	\frac{d}{dx}(6\cos^{4}(3x+2))
inverse oflaplace x^2+1	inverselaplace\:x^{2}+1
y^{''}-3y^'+2y=0,y(0)=1,y^'(0)=-1	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=0,y(0)=1,y^{\prime\:}(0)=-1
(d^2y)/(dx^2)-5(dy)/(dx)+6y=5e^{3x}	\frac{d^{2}y}{dx^{2}}-5\frac{dy}{dx}+6y=5e^{3x}
inverse oflaplace ((10s-3))/(s^2+4s+29)	inverselaplace\:\frac{(10s-3)}{s^{2}+4s+29}
integral of x/((1+4x^2)^2)	\int\:\frac{x}{(1+4x^{2})^{2}}dx
f(x)=sqrt(4x+10)	f(x)=\sqrt{4x+10}
derivative of (6x+7^2)	\frac{d}{dx}((6x+7)^{2})
integral of x^2*ln^2(x)	\int\:x^{2}\cdot\:\ln^{2}(x)dx
derivative of f(x)=(1/x-1/a)^2	derivative\:f(x)=(\frac{1}{x}-\frac{1}{a})^{2}
tangent of 7/x	tangent\:\frac{7}{x}
derivative of cosh(cos(x))	\frac{d}{dx}(\cosh(\cos(x)))
limit as x approaches 0 of (sin(2x))/(arcsin(x))	\lim\:_{x\to\:0}(\frac{\sin(2x)}{\arcsin(x)})
derivative of (x^2+5^7)	\frac{d}{dx}((x^{2}+5)^{7})
derivative of f(x)=ln(e^{-x}+xe^{-x})	derivative\:f(x)=\ln(e^{-x}+xe^{-x})
derivative of (3t^5-1)/(x^2+2)	derivative\:\frac{3t^{5}-1}{x^{2}+2}
integral of 10t^2+7t-9	\int\:10t^{2}+7t-9dt
integral of ((2y-5)-y)/(y+xy)	\int\:\frac{(2y-5)-y}{y+xy}dx
derivative of sqrt(2x+x^2)	\frac{d}{dx}(\sqrt{2x+x^{2}})
derivative of sqrt(2)cos(x-sqrt(2))	\frac{d}{dx}(\sqrt{2}\cos(x)-\sqrt{2})
inverse oflaplace (s+2)/(s+4)	inverselaplace\:\frac{s+2}{s+4}
(\partial)/(\partial y)(x^{4y})	\frac{\partial\:}{\partial\:y}(x^{4y})
limit as x approaches-infinity of ((sqrt(5x^2-2)))/(x+3)	\lim\:_{x\to\:-\infty\:}(\frac{(\sqrt{5x^{2}-2})}{x+3})
area y=x^2-8,y=7-2x	area\:y=x^{2}-8,y=7-2x
limit as x approaches 0 of (\|x-1\|-1)/x	\lim\:_{x\to\:0}(\frac{\left\|x-1\right\|-1}{x})
limit as x approaches 0+of ax^{x^2}	\lim\:_{x\to\:0+}(ax^{x^{2}})
limit as x approaches 3 of 4x^3-5x^2+x-8	\lim\:_{x\to\:3}(4x^{3}-5x^{2}+x-8)
integral of sec^2(x)-csc(x)cot(x)	\int\:\sec^{2}(x)-\csc(x)\cot(x)dx
limit as x approaches-3 of f(x)x	\lim\:_{x\to\:-3}(f(x)x)
integral of (4x)/(sqrt(16-x^4))	\int\:\frac{4x}{\sqrt{16-x^{4}}}dx
y^'=8y^2cos(t)+7y^2sin(4t)	y^{\prime\:}=8y^{2}\cos(t)+7y^{2}\sin(4t)
tangent of x^3-2x+2	tangent\:x^{3}-2x+2
integral of sin(4x)cos(17x)	\int\:\sin(4x)\cos(17x)dx
sum from n=0 to infinity}(2/(\sqrt{11) of)^n	\sum\:_{n=0}^{\infty\:}(\frac{2}{\sqrt{11}})^{n}
tangent of-6x^2+5x	tangent\:-6x^{2}+5x
derivative of y=(ln(x))^3	derivative\:y=(\ln(x))^{3}
integral of (sqrt(x+3))/(x-1)	\int\:\frac{\sqrt{x+3}}{x-1}dx
derivative of f(x)=e^{2-x}	derivative\:f(x)=e^{2-x}
(\partial)/(\partial x)(e^{-x}tan(y))	\frac{\partial\:}{\partial\:x}(e^{-x}\tan(y))
integral of+(54)/(1-cos(9x))	\int\:+\frac{54}{1-\cos(9x)}dx

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