alleryStart learning →Which function has 1/(1 + x^2) as its derivative?
- log(1 + x^2) + c
- tan^-1 x + c
- -tan^-1 x + c
- sin^-1 x + c
Show answer and solution
Correct answer: B. tan^-1 x + c
The derivative of tan^-1 x is 1/(1 + x^2).
MHT-CET Indefinite Integration — practice questions — page 2
Explore 70 free Indefinite Integration questions in MHT-CET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–60 of 70.
Which function has 1/(1 + x^2) as its derivative?Read the answer and worked solution →What standard function integrates 1/sqrt(1 - x^2)?Read the answer and worked solution →Putting x = a tan t, 1/(x^2 + a^2) integrates to what?Read the answer and worked solution →Which standard result applies to 1/(x^2 - a^2)?Read the answer and worked solution →Using x = a tan t, how does 1/sqrt(x^2 + a^2) integrate?Read the answer and worked solution →What standard formula gives 1/sqrt(a^2 - x^2) integrated?Read the answer and worked solution →With a = 3, what is the primitive of 1/(x^2 + 9)?Read the answer and worked solution →With a = 5, which function integrates 1/sqrt(25 - x^2)?Read the answer and worked solution →After completing the square, how does 1/(x^2 + 2x + 5) integrate?Read the answer and worked solution →When is integration by parts most useful?Read the answer and worked solution →Taking x as the first function, what is the integral of x e^x?Read the answer and worked solution →Using parts with u = x, how does x sin x integrate?Read the answer and worked solution →Writing log x as 1 times log x, what is its antiderivative?Read the answer and worked solution →Taking log x as first function, how does x log x integrate?Read the answer and worked solution →Repeated parts applied to x^2 e^x give which result?Read the answer and worked solution →What is the integral of e^x times the sum f(x) + f'(x)?Read the answer and worked solution →Writing f = sin x, how does e^x (sin x + cos x) integrate?Read the answer and worked solution →Taking f = 1/x, what is the antiderivative of e^x (1/x - 1/x^2)?Read the answer and worked solution →Parts applied twice to e^x sin x lead to which result?Read the answer and worked solution →Which expression is the primitive of x e^(2x)?Read the answer and worked solution →When x is replaced by phi(t), dx is replaced by which expression?Read the answer and worked solution →If f integrates to g(x) + c, how does f(ax + b) integrate?Read the answer and worked solution →A square root of the linear form 2x + 3 integrates to what?Read the answer and worked solution →What is the antiderivative of the reciprocal root 1/sqrt(4x + 1)?Read the answer and worked solution →Using t = log x, what is the integral of sin(log x) over x?Read the answer and worked solution →Put t = tan^-1 x. What does e^(tan^-1 x)/(1 + x^2) integrate to?Read the answer and worked solution →The ratio sec^2 x over tan x has which antiderivative?Read the answer and worked solution →How does the function x^(-1/2) integrate?Read the answer and worked solution →Multiplying by e^x top and bottom, 1/(e^x + e^(-x)) integrates to what?Read the answer and worked solution →A rational function f(x)/g(x) is proper whenRead the answer and worked solution →
Worked practice questions
What standard function integrates 1/sqrt(1 - x^2)?
- sin^-1 x + c
- cos^-1 x + c
- tan^-1 x + c
- sec^-1 x + c
Show answer and solution
Correct answer: A. sin^-1 x + c
The derivative of sin^-1 x is 1/sqrt(1 - x^2).
Putting x = a tan t, 1/(x^2 + a^2) integrates to what?
- (1/a) tan^-1(x/a) + c
- a tan^-1(x/a) + c
- (1/2a) log|x - a| + c
- (1/a) sin^-1(x/a) + c
Show answer and solution
Correct answer: A. (1/a) tan^-1(x/a) + c
Substituting x = a tan t gives dx = a sec^2 t dt, leaving (1/a) times t.
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