List of top Mathematics Questions on Indefinite Integrals asked in CBSE CLASS XII

Find : \( \int \frac{x - \sin x}{1 - \cos x} \, dx \).

Evaluate : \( \int_0^2 \frac{1}{\sqrt{x^2 + 2x + 3}} \, dx \).

\( \int \sqrt{\frac{1 + \cos x}{1 - \cos x}} \, dx \) is equal to :

Find : \( \int \frac{x - \sin x}{1 - \cos x} \, dx \)

Evaluate : \( \int_0^2 \frac{1}{\sqrt{x^2 + 2x + 3}} \, dx \)

\( \int \frac{1}{\sqrt{1 + \cos 2x}} \, dx \) is equal to :

\(\int \frac{dx}{\sqrt{25 - 16x^2}}\) is equal to :

Find : \( \int \frac{\cos x}{(2 + \sin x)(4 + \sin x) \, dx \)}

Find : \( \int \frac{x + 3}{x^2 + 4x + 5} \, dx \)

\(\int \frac{dx}{2^x + 2^{-x}}\) is equal to :

If \( \frac{d}{dx} (F(x)) = \frac{1{e^x + 1} \), then find F(x) given that F(0) = log \( \frac{1}{2} \).}

The indefinite integral \(\int \frac{dx}{\sqrt{25 - 16x^2}}\) is equal to:

If \[ \frac{d}{dx}\bigl(F(x)\bigr)=\frac{1}{e^x+1}, \] then find \(F(x)\), given that the initial condition is \[ F(0)=\log_e\!\left(\frac{1}{2}\right). \]

Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]

Evaluate the definite integral: \[ \int_0^{\frac{\pi}{2}} \frac{\sin x}{1 + \cos^2 x} \, dx \]

Find the area of triangle ABC bounded by:
5x −2y−10 =0, x−y−9=0, 3x−4y−6=0, usingintegrationmethod.

Evaluate: \[ \int_{1}^{3} (|x - 1| + |x - 2|) dx. \]

Find the integral:
\[ I = \int \frac{\cos \theta \, d\theta}{\sqrt{3 - 3\sin \theta - \cos^2 \theta}} \]

Find: \[ I = \int \frac{2x^2 + 1}{x^2(x^2 + 4)} \, dx \]

Evaluate: \[ I = \int_{0}^{\pi/2} \frac{ x \sin x \cos x }{ \sin^4 x + \cos^4 x } \, dx. \]

The value of $\displaystyle \int_{0}^{\pi/6} \sin 3x \, dx$ is: